innerProductSpace π | CompOp | 460 mathmath: Matrix.l2_opNorm_toEuclideanCLM, OrthonormalBasis.singleton_repr, Pi.comul_eq_adjoint, TemperedDistribution.lineDerivOpCLM_eq, MeasureTheory.Lp.toTemperedDistributionCLM_apply, UpperHalfPlane.mdifferentiable_num, TemperedDistribution.fourierInv_toTemperedDistributionCLM_eq, hasSum_mellin_pi_mul_sq', TensorProduct.enorm_lid, continuousOn_stereoToFun, CuspFormClass.holo, InnerProductSpace.toLinearIsometry_toDual, MeasureTheory.charFun_eq_fourierIntegral', PeriodPair.hasFPowerSeriesAt_weierstrassPExcept, hasFDerivAt_iff_hasGradientAt, Real.fourierCoeff_tsum_comp_add, UnitAddTorus.coe_mFourierBasis, ModularFormClass.qExpansionFormalMultilinearSeries_apply_norm, ModularFormClass.hasFPowerSeries_cuspFunction, ModularFormClass.qExpansionFormalMultilinearSeries_radius, InnerProductSpace.rankOne_one_left_eq_innerSL, EuclideanSpace.orthonormal_single, PeriodPair.coeff_weierstrassPExceptSeries, Complex.meromorphic_digamma, OrthonormalBasis.repr_injective, PeriodPair.iteratedDeriv_weierstrassPExcept_self, Complex.GammaIntegral_eq_mellin, norm_jacobiThetaβ_term_fderiv_ge, Matrix.spectrum_toEuclideanLin, Matrix.cstar_nnnorm_def, Matrix.l2_opNorm_mulVec, one_add_cpow_hasFPowerSeriesAt_zero, inner_apply', AddChar.wInner_cWeight_self, innerSL_apply_apply, LinearMap.adjoint_innerββ_apply, EuclideanSpace.inner_single_left, EuclideanSpace.basisFun_toBasis, ContinuousLinearMap.innerSL_apply_comp_of_isSymmetric, circleIntegral.integral_sub_inv_of_mem_ball, fourierCoeffOn.const_mul, mellin_div_const, TemperedDistribution.lineDerivOp_fourier_eq, Matrix.spectrum_toLpLin, InnerProductSpace.toDual_symm_apply, EuclideanSpace.basisFun_apply, fourierIntegral_gaussian_innerProductSpace', MeasureTheory.charFun_toDual_symm_eq_charFunDual, fourier_gaussian_pi', MeasureTheory.charFun_eq_fourierIntegral, Differentiable.fderiv_norm_rpow, TemperedDistribution.smulLeftCLM_compL_smulLeftCLM, PeriodPair.iteratedDeriv_derivWeierstrassPExcept_self, TensorProduct.toLinearEquiv_lidIsometry, OrthonormalBasis.toBasis_singleton, Matrix.IsHermitian.eigenvalues_eq, HasFDerivAt.norm_sq, OrthonormalBasis.repr_self, differentiableOn_iteratedDerivWithin_cotTerm, HarmonicAt.analyticAt_complex_partial, OrthonormalBasis.measurePreserving_repr, SchwartzMap.integral_fourierInv_smul_eq, PeriodPair.analyticAt_weierstrassPExcept, summableLocallyUniformlyOn_iteratedDerivWithin_cotTerm, Matrix.IsHermitian.eigenvectorUnitary_col_eq, ContinuousLinearMap.toSesqForm_apply_coe, fourier_gaussian_innerProductSpace, Matrix.toEuclideanLin_apply, TemperedDistribution.smulLeftCLM_neg, Function.HasTemperateGrowth.toTemperedDistribution_apply, LSeries_iteratedDeriv, Complex.analyticOnNhd_univ_iff_differentiable, Pi.counit_eq_adjoint, ProbabilityTheory.covarianceBilin_apply_basisFun_self, Complex.taylorSeries_eq_on_ball', fourierCoeff_bernoulli_eq, LDL.lowerInv_orthogonal, AddChar.wInner_cWeight_eq_zero_iff_ne, TemperedDistribution.instLineDerivLeftSMulReal, EuclideanSpace.instFactEqNatFinrankFin, differentiable_euclidean, TemperedDistribution.fourierInv_lineDerivOp_eq, UpperHalfPlane.mdifferentiable_inv_denom, contDiffWithinAt_euclidean, Real.fourier_iteratedFDeriv, InnerProductSpace.toDualMap_apply_apply, UnitAddTorus.mFourierCoeff_toLp, Matrix.IsHermitian.eigenvectorUnitary_mulVec, TemperedDistribution.instFourierAdd, coe_innerSL_apply, PeriodPair.hasFPowerSeriesAt_derivWeierstrassPExcept, LSeries_analyticOnNhd, TemperedDistribution.instFourierSMul, TensorProduct.lidIsometry_apply, Module.Basis.coe_toOrthonormalBasis_repr, orthonormal_fourier, UpperHalfPlane.contMDiff_coe, CuspForm.holo', Differentiable.hasFPowerSeriesOnBall, BoundedContinuousFunction.mem_charPoly, HasGradientWithinAt.differentiableWithinAt, TemperedDistribution.delta_apply, PeriodPair.analyticOnNhd_derivWeierstrassPExcept, fourierIntegral_gaussian_pi, hasSum_mellin, iteratedDerivWithin_cot_pi_mul_eq_mul_tsum_div_pow, hasGradientWithinAt_iff_hasFDerivWithinAt, DifferentiableOn.contDiffOn, TemperedDistribution.instContinuousFourier, LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, OrthonormalBasis.coe_ofRepr, UpperHalfPlane.contMDiff_inv_denom, Complex.orthonormalBasisOneI_repr_apply, SchwartzMap.delta_apply, norm_cauchyPowerSeries_le, hasFDerivAt_norm_rpow, fourier_gaussian_innerProductSpace', Matrix.toEuclideanCLM_toLp, hasSum_fourier_series_L2, ProbabilityTheory.iteratedDeriv_complexMGF, contDiffOn_stereoToFun, HilbertBasis.hasSum_repr, HasFDerivWithinAt.hasGradientWithinAt, innerSL_inj, StrongDual.toLp_of_not_memLp, TensorProduct.inner_lid_lid, Matrix.piLp_ofLp_toEuclideanLin, InnerProductSpace.toDual_apply, OrthonormalBasis.tensorProduct_repr_tmul_apply', Matrix.l2_opNNNorm_mulVec, InnerProductSpace.toDualMap_apply, ProbabilityTheory.analyticAt_complexMGF, HurwitzZeta.hurwitzEvenFEPair_zero_symm, circleIntegral.integral_sub_zpow_of_undef, PeriodPair.weierstrassPExcept_eq_tsum, Orthonormal.isHilbertSum, OrthonormalBasis.singleton_apply, OrthonormalBasis.equiv_apply, TemperedDistribution.fourier_toTemperedDistributionCLM_eq, Module.Basis.coe_toOrthonormalBasis_repr_symm, InnerProductSpace.toDual_apply_apply, ContinuousLinearMap.adjointAux_apply, ProperCone.innerDual_singleton, PeriodPair.meromorphic_derivWeierstrassP, InnerProductSpace.rankOne_def, stereoToFun_apply, TemperedDistribution.fourierTransformInv_toTemperedDistributionCLM_eq, OrthonormalBasis.repr_apply_apply, ClosedSubmodule.orthogonal_eq_inter, MeasureTheory.L2.inner_indicatorConstLp_one, SchwartzMap.toTemperedDistributionCLM_apply_apply, TemperedDistribution.smulLeftCLM_sub, Complex.one_add_cpow_hasFPowerSeriesAt_zero, UpperHalfPlane.contMDiff_num, UpperHalfPlane.mdifferentiable_denom, LinearMap.toMatrix_innerββ_apply, wInner_one_eq_inner, Matrix.PosSemidef.toLinearMapβ'_zero_iff, contDiffAt_euclidean, innerSLFlip_apply_apply, eqOn_iteratedDerivWithin_cotTerm_upperHalfPlaneSet, finrank_euclideanSpace, Complex.one_div_sub_sq_hasFPowerSeriesOnBall_zero, InnerProductSpace.continuousLinearMapOfBilin_zero, ContinuousLinearMap.toLinearMap_innerSL_apply, contDiffOn_euclidean, HasGradientAt.hasFDerivAt, Real.fourier_fderiv, eqOn_iteratedDeriv_cotTerm, HasFDerivWithinAt.norm_sq, Complex.one_div_one_sub_pow_hasFPowerSeriesOnBall_zero, Orthonormal.linearIsometryEquiv_symm_apply_single_one, UnitAddTorus.orthonormal_mFourier, Matrix.ofLp_toEuclideanCLM, fourierCoeff_toLp, coe_fourierBasis, AddChar.wInner_cWeight_eq_one_iff_eq, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, ModularFormClass.qExpansion_coeff, inner_tmul_eq, hasSum_sq_fourierCoeffOn, torusIntegral_const_mul, differentiableWithinAt_euclidean, Matrix.isPositive_toEuclideanLin_iff, HasGradientAt.differentiableAt, hasSum_mellin_pi_mul, le_radius_cauchyPowerSeries, wInner_const_left, wInner_cWeight_const_left, MeasureTheory.integral_condExpL2_eq_of_fin_meas_real, hasStrictFDerivAt_norm_sq, LinearMap.adjoint_toSpanSingleton, hasMellin_one_Ioc, TemperedDistribution.instLineDerivSMulReal, inner_apply, MeasureTheory.Measure.toTemperedDistribution_apply, Complex.analyticOn_iff_differentiableOn, InnerProductSpace.nullSubmodule_le_ker_toDualMap_left, norm_wInner_le, LinearMap.IsSymmetric.eigenvectorBasis_apply_self_apply, TemperedDistribution.fourier_lineDerivOp_eq, Matrix.l2_opNNNorm_def, TemperedDistribution.fourier_delta_zero, PeriodPair.order_weierstrassP, MeromorphicNFOn.Gamma, iteratedDerivWithin_cot_pi_mul_eq_mul_tsum_zpow, EuclideanSpace.basisFun_repr, UnitAddTorus.instContinuousSMulComplexSubtypeAEEqFunVolumeMemAddSubgroupLp, OrthonormalBasis.equiv_apply_euclideanSpace, TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq, Complex.orthonormalBasisOneI_repr_symm_apply, UnitAddTorus.hasSum_mFourier_series_L2, TemperedDistribution.laplacian_eq_sum, HasGradientWithinAt.fderivWithin_apply, TemperedDistribution.instContinuousLineDeriv, Complex.one_div_sub_pow_hasFPowerSeriesOnBall_zero, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, wInner_const_right, InnerProductSpace.rankOne_def', Complex.HadamardThreeLines.diffContOnCl_interpStrip, Matrix.IsHermitian.eigenvectorUnitary_apply, hasFPowerSeriesOn_cauchy_integral, UpperHalfPlane.contMDiff_denom_zpow, Complex.circleIntegral_div_sub_of_differentiable_on_off_countable, EuclideanSpace.inner_eq_star_dotProduct, DifferentiableOn.hasFPowerSeriesOnBall, OrthonormalBasis.sum_repr_symm, Complex.analyticOn_univ_iff_differentiable, fourierIntegral_gaussian_innerProductSpace, Differentiable.contDiff, InnerProductSpace.innerSL_norm, HurwitzZeta.hurwitzOddFEPair_fβ, cot_pi_mul_contDiffWithinAt, TemperedDistribution.smulLeftCLM_add, PeriodPair.coeff_weierstrassPSeries, ProbabilityTheory.covarianceBilin_apply_basisFun, hasGradientAt_iff_hasFDerivAt, locallyFinsuppWithin.logCounting_divisor, HilbertBasis.repr_symm_single, HilbertBasis.repr_apply_apply, HurwitzZeta.hurwitzOddFEPair_Ξ΅, OrthonormalBasis.measurePreserving_repr_symm, EuclideanSpace.piLpCongrLeft_single, hasFDerivWithinAt_euclidean, Matrix.IsHermitian.eigenvectorUnitary_coe, TemperedDistribution.fourierTransform_apply, Matrix.toEuclideanLin_eq_toLin, Matrix.isHermitian_iff_isSymmetric, hasSum_mellin_pi_mulβ, EuclideanSpace.basisFun_inner, Real.fourierIntegral_fderiv, InnerProductSpace.toMatrix_rankOne, differentiableAt_euclidean, PeriodPair.hasFPowerSeriesOnBall_weierstrassP, harmonic_is_realOfHolomorphic, PeriodPair.weierstrassPSeries_hasSum, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, span_fourierLp_closure_eq_top, circleIntegral.integral_sub_zpow_of_ne, LSeries.iteratedDeriv_alternating, differentiableOn_euclidean, ContinuousLinearMap.adjoint_toSpanSingleton, circleIntegral.integral_smul_const, SchwartzMap.integral_fourier_mul_eq, PeriodPair.hasFPowerSeriesOnBall_derivWeierstrassPExcept, wInner_one_const_right, Matrix.ofLp_toEuclideanLin_apply, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, Polynomial.fourierCoeff_toAddCircle_natCast, EuclideanSpace.inner_basisFun_real, innerSLFlip_apply, fourierCoeffOn_of_hasDerivAt_Ioo, InnerProductSpace.toContinuousLinearMap_toDualMap, OrthonormalBasis.repr_symm_single, innerSL_apply_norm, InnerProductSpace.toDual_apply_eq_toDualMap_apply, PeriodPair.analyticOnNhd_derivWeierstrassP, hasFPowerSeriesOnBall_cuspFunction, tsum_sq_fourierCoeffOn, ModularFormClass.qExpansion_coeff_eq_circleIntegral, MeasureTheory.L2.inner_indicatorConstLp_one_indicatorConstLp_one, TensorProduct.norm_lid, MeasureTheory.charFun_eq_charFunDual_toDualMap, Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zero, PeriodPair.meromorphic_weierstrassP, toMatrix_innerSL_apply, PeriodPair.analyticAt_derivWeierstrassPExcept, TemperedDistribution.instFourierInvSMul, HurwitzZeta.hurwitzOddFEPair_gβ, TemperedDistribution.instFourierInvAdd, UnitAddTorus.hasSum_prod_mFourierCoeff, circleIntegral.circleIntegral_congr_codiscreteWithin, TemperedDistribution.fourierInv_apply, HurwitzZeta.hurwitzOddFEPair_f, fourierCoeff.const_mul, TemperedDistribution.fourierTransform_toTemperedDistributionCLM_eq, one_add_cpow_hasFPowerSeriesOnBall_zero, TemperedDistribution.instLineDerivAdd, TemperedDistribution.instLineDerivSMulComplex, LSeries_analyticOn, HilbertBasis.repr_self, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_triangular', Complex.one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, SchwartzMap.integral_fourierInv_mul_eq, hasFDerivWithinAt_iff_hasGradientWithinAt, TemperedDistribution.laplacian_toTemperedDistributionCLM_eq, Matrix.toEuclideanLin_apply_piLp_toLp, mdifferentiable_jacobiTheta, Orthonormal.orthogonalFamily, PeriodPair.hasFPowerSeriesOnBall_weierstrassPExcept, ProbabilityTheory.hasDerivAt_iteratedDeriv_complexMGF, SchwartzMap.integral_fourier_smul_eq, HurwitzZeta.hurwitzOddFEPair_k, UpperHalfPlane.contMDiffAt_ofComplex, wInner_one_const_left, ModularForm.holo', ProbabilityTheory.analyticOn_complexMGF, innerSL_apply, OrthonormalBasis.coe_toBasis_repr, iteratedDerivWithin_cot_sub_inv_eq_add_mul_tsum, StrongDual.toLp_apply, OrthonormalBasis.sum_repr, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, DifferentiableOn.analyticOnNhd, hasSum_sq_fourierCoeff, UpperHalfPlane.contMDiffAt_iff, UpperHalfPlane.instIsManifoldComplexModelWithCornersSelfTopWithTopENat, Complex.taylorSeries_eq_on_eball', UnitAddTorus.mFourierBasis_repr, Function.Periodic.contDiff_qParam, Complex.analyticOnNhd_iff_differentiableOn, MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot, MeasureTheory.Lp.toTemperedDistribution_toLp_eq, fourierBasis_repr, Complex.analyticAt_of_differentiable_on_punctured_nhds_of_continuousAt, MeasureTheory.BoundedContinuousFunction.inner_toLp, TemperedDistribution.laplacian_apply_apply, TemperedDistribution.smulLeftCLM_smulLeftCLM_apply, OrthonormalBasis.coe_toBasis_repr_apply, UpperHalfPlane.mdifferentiable_coe, OrthonormalBasis.coe_equiv_euclideanSpace, PeriodPair.weierstrassPExceptSeries_hasSum, ModularFormClass.analyticAt_cuspFunction_zero, TemperedDistribution.lineDerivOp_apply_apply, Complex.HadamardThreeLines.diffContOnCl_invInterpStrip, signedDist_apply, EuclideanSpace.inner_toLp_toLp, UnitAddTorus.hasSum_sq_mFourierCoeff, TemperedDistribution.lineDerivOp_fourierInv_eq, HurwitzZeta.hurwitzOddFEPair_g, HasFDerivAt.hasGradientAt, Complex.circleTransformDeriv_bound, Complex.hasFPowerSeriesOnBall_of_differentiable_off_countable, Matrix.IsHermitian.eigenvectorUnitary_transpose_apply, analyticAt_clog, AddChar.linearIndependent, ModularFormClass.holo, circleIntegral.integral_sub_center_inv, MeasureTheory.Lp.toTemperedDistribution_apply, TemperedDistribution.smulLeftCLM_const, wInner_cWeight_const_right, TemperedDistribution.smulLeftCLM_sum, fourierCoeff_liftIoc_eq, TemperedDistribution.instContinuousFourierInv, Complex.one_add_cpow_hasFPowerSeriesOnBall_zero, AddChar.wInner_cWeight_eq_boole, EuclideanSpace.inner_single_right, TemperedDistribution.fourier_apply, hasMellin_cpow_Ioc, EisensteinSeries.eisensteinSeries_SIF_MDifferentiable, tsum_sq_fourierCoeff, Submodule.orthogonal_eq_inter, VectorFourier.integral_fourierIntegral_smul_eq_flip, SchwartzMap.coe_apply, DifferentiableOn.analyticAt, fderiv_norm_rpow, Matrix.toEuclideanLin_eq_toLin_orthonormal, Complex.one_div_one_sub_hasFPowerSeriesOnBall_zero, UpperHalfPlane.mdifferentiableAt_iff, OrthonormalBasis.coe_singleton, fourierCoeffOn_of_hasDerivAt, PeriodPair.analyticOnNhd_weierstrassPExcept, TemperedDistribution.smulLeftCLM_smul, ArithmeticFunction.iteratedDeriv_LSeries_alternating, InnerProductSpace.continuousLinearMapOfBilin_apply, Matrix.cstar_norm_def, SchwartzMap.tsum_eq_tsum_fourierIntegral, inner_matrix_row_row, HasGradientAt.fderiv_apply, TemperedDistribution.derivCLM_apply_apply, Complex.taylorSeries_eq_of_entire', Meromorphic.Gamma, innerSL_apply_coe, ProbabilityTheory.analyticOnNhd_complexMGF, MeasureTheory.ContinuousMap.inner_toLp, gradient_eq_deriv, TemperedDistribution.fourierTransformInv_apply, ModularFormClass.qExpansionFormalMultilinearSeries_coeff, UpperHalfPlane.contMDiff_smul, TensorProduct.nnnorm_lid, eqOn_iteratedDerivWithin_cotTerm_integerComplement, Matrix.IsHermitian.mulVec_eigenvectorBasis, Matrix.l2_opNorm_def, wInner_nonneg, Matrix.toEuclideanLin_toLp, UpperHalfPlane.contMDiff_denom, norm_innerSL_le, BoundedContinuousFunction.separatesPoints_charPoly, Complex.one_div_sub_sq_sub_one_div_sq_hasFPowerSeriesOnBall_zero, EisensteinSeries.eisensteinSeriesSIF_mdifferentiable, UnitAddTorus.span_mFourierLp_closure_eq_top, PeriodPair.analyticOnNhd_weierstrassP, UpperHalfPlane.mdifferentiable_denom_zpow, HasGradientWithinAt.hasFDerivWithinAt, Pi.orthonormalBasis_repr, MeromorphicOn.Gamma, Polynomial.fourierCoeff_toAddCircle, Complex.hasFPowerSeriesOnBall_ofScalars_mul_add_zero, UpperHalfPlane.mdifferentiable_iff, Real.fourierIntegral_iteratedFDeriv, Complex.analyticAt_iff_eventually_differentiableAt, finrank_euclideanSpace_fin, fourierCoeffOn_of_hasDeriv_right, OrthonormalBasis.repr_reindex, Matrix.IsHermitian.star_eigenvectorUnitary_mulVec, InnerProductSpace.symm_toEuclideanLin_rankOne, ContinuousLinearMap.adjoint_innerSL_apply, UpperHalfPlane.mdifferentiableAt_ofComplex, fourier_gaussian_pi, Real.fourier_smul_convolution_eq, MeasureTheory.condExpL2_const_inner, TemperedDistribution.laplacianCLM_apply, Complex.taylorSeries_eq_on_emetric_ball', fourierCoeff_liftIco_eq, contDiff_euclidean, fderiv_norm_sq_apply, OrthonormalBasis.tensorProduct_repr_tmul_apply, circleIntegral.integral_const_mul, MeasureTheory.Lp.toTemperedDistribution_smul_eq, inner_eq_wInner_one, Differentiable.analyticAt, fderiv_norm_sq, Complex.one_div_sub_hasFPowerSeriesOnBall_zero, ContinuousLinearMap.innerSL_apply_comp, TensorProduct.lidIsometry_symm_apply, fourierIntegral_gaussian_pi', ContinuousLinearMap.toSesqForm_apply_norm_le, HilbertBasis.hasSum_repr_symm, InnerProductSpace.nullSubmodule_le_ker_toDualMap_right, TemperedDistribution.smulLeftCLM_apply_apply, hasSum_mellin_pi_mul_sq, inner_matrix_col_col, BoundedContinuousFunction.char_mem_charPoly, SchwartzMap.tsum_eq_tsum_fourier, norm_jacobiThetaβ_term_fderiv_le, UpperHalfPlane.mdifferentiable_smul, Polynomial.fourierCoeff_toAddCircle_eq_zero_of_lt_zero, DifferentiableOn.analyticOn, hasStrictFDerivAt_euclidean, fourierCoeff_fourier
|
toInnerProductSpaceReal π | CompOp | 1254 mathmath: Real.hasDerivAt_fourier, ProbabilityTheory.variance_eq_integral, NumberField.mixedEmbedding.fundamentalDomain_integerLattice, MeasureTheory.Integrable.integral_norm_prod_right, MeasureTheory.mulEquivHaarChar_smul_integral_map, Bundle.ContMDiffRiemannianMetric.isVonNBounded, Polynomial.mahlerMeasure_def_of_ne_zero, Bundle.ContMDiffRiemannianMetric.contMDiff, SmoothBumpCovering.toSmoothPartitionOfUnity_eq_mul_prod, ContDiffBump.ae_convolution_tendsto_right_of_locallyIntegrable, MonotoneOn.intervalIntegral_slope_le, ProbabilityTheory.condIndepFun_iff_condExp_inter_preimage_eq_mul, ProbabilityTheory.isGaussian_iff_gaussian_charFun, exists_contMDiffMap_zero_one_of_isClosed, InformationTheory.integral_llr_add_mul_log_nonneg, NumberField.mixedEmbedding.normAtComplexPlaces_mixedSpaceOfRealSpace, mellin_eq_fourier, integral_cos, ProbabilityTheory.condDistrib_ae_eq_condExp, Real.hasFDerivAt_fourierChar_neg_bilinear_left, instIsManifoldRealEuclideanSpaceFinModelWithCornersSelfTopWithTopENatElemHAddNatOfNatSphere, Function.hasTemperateGrowth_inner_right, NumberField.Units.finrank_eq_rank, ValueDistribution.proximity_zero, Real.fourierCoeff_tsum_comp_add, tendsto_tsum_div_pow_atTop_integral, Manifold.pathELength_eq_lintegral_mfderiv_Ioo, ZSpan.volume_real_fundamentalDomain, Complex.areaForm, Real.hasDerivAt_sigmoid, ProbabilityTheory.analyticOn_mgf, MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul_of_measurable_of_sigmaFinite, Matrix.IsHermitian.det_abs, ProbabilityTheory.condIndep_iff, deriv_abs, integral_sin_mul_cosβ, ProbabilityTheory.covarianceBilinDual_apply', ProbabilityTheory.hasGaussianLaw_iff_charFunDual_map_eq, contDiffAt_norm_smul_iff, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_ne, intervalIntegral.mul_integral_comp_mul_sub, AnalyticOn.im_ofReal, AbsolutelyContinuousOnInterval.integral_deriv_eq_sub, intervalIntegral.integral_hasFDerivAt_of_tendsto_ae, Polynomial.Chebyshev.integral_measureT_eq_integral_cos, integral_const_on_unit_interval, integral_exp_mul_Iic, MeasureTheory.submartingale_iff_expected_stoppedValue_mono, ZLattice.covolume_eq_det_inv, ProbabilityTheory.covarianceBilinDual_apply, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, ProbabilityTheory.IsGaussian.map_eq_gaussianReal, MeasureTheory.integral_fintype_prod_volume_eq_pow, Real.fderiv_fourierChar_neg_bilinear_right_apply, ConvexOn.map_set_average_le, intervalIntegral.fderiv_integral_of_tendsto_ae, flip_innerSL_real, LipschitzWith.memLp_lineDeriv, AnalyticOnNhd.re_ofReal, SmoothPartitionOfUnity.contMDiffAt_finsum, differentiableWithinAt_abs_pos, MeasureTheory.condExpL2_ae_eq_zero_of_ae_eq_zero, LipschitzWith.ae_lineDeriv_sum_eq, Orientation.inner_mul_inner_add_areaForm_mul_areaForm, intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right, Orientation.areaForm_le, DifferentiableWithinAt.norm, det_fderivPolarCoordSymm, SmoothPartitionOfUnity.locallyFinite, exists_smooth_one_nhds_of_subset_interior, ProbabilityTheory.covarianceBilin_apply_eq_cov, ProbabilityTheory.covarianceBilin_self, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, SmoothPartitionOfUnity.nonneg, hasDerivAt_bernoulliFun, Orientation.volumeForm_neg_orientation, ProbabilityTheory.sum_prob_mem_Ioc_le, MeasureTheory.pdf.integral_mul_eq_integral, GaussianFourier.integral_cexp_neg_mul_sq_norm_add_of_euclideanSpace, ProbabilityTheory.uncenteredCovarianceBilin_apply, contMDiff_neg_sphere, not_differentiableAt_norm_zero, circleAverage_log_norm_sub_constβ, BoxIntegral.unitPartition.mem_smul_span_iff, exists_eq_const_mul_intervalIntegral_of_nonneg, ContDiffBump.integral_normed, MeasureTheory.integral_fintype_prod_eq_prod, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, SmoothBumpCovering.exists_immersion_euclidean, IsOpen.exists_msmooth_support_eq, IsOpen.exists_smooth_support_eq, SmoothPartitionOfUnity.locallyFinite', Real.rpow_eq_const_mul_integral, interval_average_eq_div, Bundle.RiemannianMetric.isVonNBounded, ProbabilityTheory.setIntegral_condCDF, integral_pow, fourier_gaussian_pi', Matrix.PosSemidef.sqrt_eq_zero_iff, ProbabilityTheory.integral_continuousLinearMap_gaussianReal, Differentiable.fderiv_norm_rpow, integral_log_sin_zero_pi_div_two, lintegral_fderiv_lineMap_eq_edist, exists_eq_interval_average_of_noAtoms, MeasureTheory.Measure.addHaarScalarFactor_eq_integral_div, ConvexOn.set_average_mem_epigraph, signedDist_right_congr, StrictConcaveOn.ae_eq_const_or_lt_map_average, intervalIntegral.integral_ofReal, ProbabilityTheory.hasGaussianLaw_iff_charFun_map_eq, MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul, ContDiffOn.inner, integral_exp, integral_inv_of_pos, Affine.Simplex.sign_signedInfDist_lineMap_incenter_touchpoint, Module.Basis.parallelepiped_basisFun, SchwartzMap.laplacianCLM_eq, MeasureTheory.hasFiniteIntegral_prod_iff', Real.vector_fourierIntegral_eq_integral_exp_smul, Real.fourier_real_eq_integral_exp_smul, ProbabilityTheory.cdf_paretoMeasure_eq_integral, differentiableWithinAt_abs, LocallyBoundedVariationOn.ae_differentiableWithinAt, integral_sin_pow_three, Real.hasFPowerSeriesOnBall_ofScalars_mul_add_zero, instIsManifoldRealEuclideanSpaceFinOfNatNatEuclideanHalfSpaceModelWithCornersEuclideanHalfSpaceElemIcc, circleAverage_log_norm_sub_const_of_mem_closedBall, hasStrictDerivAt_abs_pos, hasDerivWithinAt_abs_pos, HasFDerivAt.norm_sq, ProbabilityTheory.IsRatCondKernelCDF.setIntegral, analyticOnNhd_circleMap, antideriv_bernoulliFun, NumberField.mixedEmbedding.commMap_apply_of_isComplex, differentiableAt_sigmoid, ProbabilityTheory.IsCondKernelCDF.integral, intervalIntegral.integral_mono_on, abs_setIntegral_mulExpNegMulSq_comp_sub_le_mul_measure, MeasureTheory.L2.inner_def, Orientation.volumeForm_map, Icc_isBoundaryPoint_bot, Polynomial.Chebyshev.integral_T_real_mul_self_measureT_of_ne_zero, deriv_abs_neg, ProbabilityTheory.moment_one, integral_exp_neg_mul_rpow, MeasureTheory.BorelCantelli.martingalePart_process_ae_eq, Polynomial.Chebyshev.integral_measureT, intervalIntegral.integral_div, integral_sin_pow_pos, signedDist_left_congr, Complex.integral_rpow_mul_exp_neg_rpow, OrthonormalBasis.measurePreserving_repr, InformationTheory.leftDeriv_klFun_one, integral_Ioi_rpow_of_lt, exists_smooth_tsupport_subset, MeasureTheory.withDensityα΅₯_eq_withDensity_pos_part_sub_withDensity_neg_part, signedDist_triangle, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_integrableOn, ProbabilityTheory.gammaCDFReal_eq_integral, integral_bernoulliFun, enorm_fderiv_norm_rpow_le, LocallyBoundedVariationOn.ae_differentiableAt, MeasurableEquiv.withDensity_ofReal_map_symm_apply_eq_integral_abs_det_fderiv_mul, MonotoneOn.intervalIntegrable_deriv, MeasureTheory.AEStronglyMeasurable.ae_integrable_condKernel_iff, Real.Icc_mem_vitaliFamily_at_left, Orientation.abs_volumeForm_apply_of_orthonormal, ContDiffBump.normed_def, signedDist_linear_apply_apply, setIntegral_Ioi_zero_rpow, integral_rpow_mul_exp_neg_rpow, NumberField.mixedEmbedding.negAt_apply_snd, MeasureTheory.measure_lt_one_eq_integral_div_gamma, MeasureTheory.setIntegral_prod_mul, Real.one_add_rpow_hasFPowerSeriesOnBall_zero, Polynomial.Chebyshev.integral_measureT_eq_integral_cos_of_continuous, VectorFourier.fourierPowSMulRight_eq_comp, MeasureTheory.charFunDual_eq_charFun_map_one, MeasureTheory.integral_fintype_prod_eq_pow, mfderivWithin_projIcc_one, intervalIntegral.integral_pos_iff_support_of_nonneg_ae', integral_cos_pow, AnalyticAt.harmonicAt_im, ProbabilityTheory.integral_stieltjesOfMeasurableRat, MeasureTheory.Measure.integral_isAddLeftInvariant_eq_smul_of_hasCompactSupport, ProbabilityTheory.IndepFun.integral_comp_mul_comp, Euclidean.closedBall_eq_image, MeasureTheory.Measure.integral_isMulLeftInvariant_isMulRightInvariant_combo, NumberField.mixedEmbedding.negAt_preimage, InformationTheory.not_differentiableWithinAt_klFun_Iio_zero, intervalIntegral.integral_mono_ae_restrict, NumberField.mixedEmbedding.iUnion_negAt_plusPart_ae, BoxIntegral.unitPartition.integralSum_eq_tsum_div, InformationTheory.toReal_klDiv_eq_integral_klFun, Quaternion.linearIsometryEquivTuple_symm_apply, Probability.integral_cauchyPDFReal, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, MeasureTheory.SignedMeasure.singularPart_smul, ProbabilityTheory.covarianceBilin_apply_basisFun_self, MeasureTheory.charFun_apply_real, Orientation.areaForm_to_volumeForm, Icc_isInteriorPoint_interior, circleAverage_log_norm_sub_const_eq_log_radius_add_posLog, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace, signedDist_le_dist, Orientation.areaForm_neg_orientation, Function.Periodic.sInf_add_zsmul_le_integral_of_pos, NumberField.mixedEmbedding.stdBasis_apply_isComplex_snd, Monotone.ae_differentiableAt, ProbabilityTheory.iCondIndep_iff, ProbabilityTheory.centralMoment_one', MeasureTheory.integral_fin_nat_prod_volume_eq_prod, MeasureTheory.condExpL2_indicator_ae_eq_smul, mfderivWithin_comp_projIcc_one, ProbabilityTheory.iCondIndepFun_iff_condExp_inter_preimage_eq_mul, SimpleGraph.lapMatrix_toLinearMapβ'_apply'_eq_zero_iff_forall_reachable, NumberField.mixedEmbedding.negAt_signSet_apply_isComplex, SmoothPartitionOfUnity.sum_finsupport', ProbabilityTheory.variance_le_sub_mul_sub, ContDiffBump.measure_closedBall_div_le_integral, signedDist_apply_apply, integral_sin_sq, SchwartzMap.integral_norm_sq_fourier, ProbabilityTheory.gaussianReal_map_continuousLinearMap, Manifold.pathELength_def, EuclideanSpace.volume_closedBall_fin_three, IccLeftChart_extend_interior_pos, Orientation.areaForm_swap, NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq, Bundle.ContinuousRiemannianMetric.symm, MeasureTheory.SignedMeasure.withDensityα΅₯_rnDeriv_eq, InformationTheory.tendsto_rightDeriv_klFun_atTop, intervalIntegral.integral_mono, MeasureTheory.Integrable.integral_norm_condDistrib_map, NumberField.mixedEmbedding.normAtComplexPlaces_polarSpaceCoord_symm, hasDerivAt_abs_neg, intervalIntegral.integral_mono_interval, MeasureTheory.condExp_smul_of_aestronglyMeasurable_right, Matrix.PosSemidef.det_sqrt, DifferentiableWithinAt.dist, hasDerivWithinAt_abs, contDiff_circleMap, intervalIntegral.integral_mono_on_of_le_Ioo, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_integral_of_antitone, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, BoundedVariationOn.intervalIntegrable_deriv, ProbabilityTheory.Kernel.setIntegral_densityProcess_of_mem, VectorFourier.hasFDerivAt_fourierIntegral, MeasureTheory.Integrable.tendsto_eLpNorm_condExp, MeasureTheory.convolution_precompR_apply, ProbabilityTheory.condIndepSets_singleton_iff, VectorFourier.fourierIntegral_iteratedFDeriv, MonotoneOn.sum_le_integral, InformationTheory.hasDerivAt_klFun, MeasureTheory.setIntegral_condExpL2_indicator, contMDiff_coe_sphere, integral_cos_pow_aux, intervalIntegral.abs_intervalIntegral_eq, InformationTheory.toReal_klDiv, ae_differentiableAt_norm, IsOpen.exists_contMDiff_support_eq_aux, NumberField.Units.instZLattice_unitLattice, Manifold.pathELength_eq_lintegral_mfderivWithin_Icc, MeasureTheory.BorelCantelli.predictablePart_process_ae_eq, ProbabilityTheory.iIndepSet.condExp_indicator_filtrationOfSet_ae_eq, ProbabilityTheory.tendsto_integral_truncation, Orientation.volumeForm_zero_pos, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_mgf', fourierIntegral_gaussian_pi, ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp, Bundle.ContinuousRiemannianMetric.continuous, ProbabilityTheory.complexMGF_mul_I, MeasureTheory.condExp_mul_of_aestronglyMeasurable_right, NumberField.Units.span_basisOfIsMaxRank, instIsManifoldRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, SmoothBumpCovering.toSmoothPartitionOfUnity_apply, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, ProbabilityTheory.Kernel.martingale_densityProcess, Complex.GammaIntegral_ofReal, mellinInv_eq_fourierIntegralInv, HasDerivWithinAt.norm_sq, MonotoneOn.integral_le_sum_Ico, PiLp.volume_preserving_toLp, InnerProductGeometry.norm_toLp_symm_crossProduct, SmoothPartitionOfUnity.contDiffAt_finsum, intervalIntegral.intervalIntegral_pos_of_pos, Chebyshev.integral_one_div_log_sq_isBigO, NumberField.Units.basisOfIsMaxRank_apply, Complex.integral_exp_neg_rpow, MeasureTheory.SignedMeasure.absolutelyContinuous_iff_withDensityα΅₯_rnDeriv_eq, ProbabilityTheory.analyticAt_mgf, NumberField.mixedEmbedding.negAt_signSet_apply_isReal, Matrix.PosSemidef.posSemidef_sqrt, orthonormalBasis_one_dim, integral_le_sum_mul_Ico_of_antitone_monotone, LipschitzWith.ae_lineDifferentiableAt, InformationTheory.leftDeriv_klFun, integral_bernoulliFun_eq_zero, LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, MeasureTheory.Integrable.tendsto_ae_condExp, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, MeasureTheory.Integrable.integral_norm_comp, ProbabilityTheory.differentiableAt_mgf, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_eq, analyticOn_log, analyticOnNhd_log, Affine.Simplex.ExcenterExists.sign_signedInfDist_touchpoint, ProbabilityTheory.iteratedDeriv_mgf, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_mgf, norm_cauchyPowerSeries_le, ProbabilityTheory.Kernel.setIntegral_densityProcess_of_le, Real.one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, mellinInv_eq_fourierInv, Metric.exists_smooth_forall_closedBall_subset, instLieGroupRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, ContDiffBump.convolution_tendsto_right, Real.fourier_real_eq, intervalIntegral.integral_lt_integral_of_continuousOn_of_le_of_exists_lt, hasDerivAt_abs_rpow, signedDist_eq_zero_of_orthogonal, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, ZSpan.volume_fundamentalDomain, ProbabilityTheory.covarianceBilin_zero, VectorFourier.differentiable_fourierIntegral, MeasureTheory.condExp_mul_of_stronglyMeasurable_right, analyticOnNhd_sigmoid, Matrix.PosSemidef.sqrt_eq_one_iff, ProbabilityTheory.integral_truncation_eq_intervalIntegral, ProbabilityTheory.condExpKernel_ae_eq_condExp', Real.deriv_Gamma_nat, ContDiff.norm_rpow, Real.fourierIntegral_convergent_iff', Matrix.PosSemidef.sqrt_sq, Bundle.ContMDiffRiemannianMetric.symm, MeasureTheory.integral_comap_eq_addEquivAddHaarChar_smul, ProbabilityTheory.analyticOnNhd_cgf, MeasureTheory.lintegral_nnnorm_condExpL2_le, SmoothPartitionOfUnity.le_one, Monotone.ae_hasDerivAt, ProbabilityTheory.IsCondKernelCDF.setIntegral, AffineSubspace.signedInfDist_eq_signedDist_of_mem, EuclideanSpace.volume_closedBall_fin_two, Affine.Simplex.signedInfDist_apply_self, VectorFourier.iteratedFDeriv_fourierIntegral, exists_contMDiffMap_zero_one_nhds_of_isClosed, ProbabilityTheory.HasCondSubgaussianMGF.ae_condExp_le, Real.one_div_one_sub_hasFPowerSeriesOnBall_zero, ContDiffBump.normed_convolution_eq_right, ProbabilityTheory.gaussianReal_map_linearMap, HasDerivWithinAt.inner, AbsolutelyContinuousOnInterval.integral_deriv_mul_eq_sub, BoxIntegral.integral_nonneg, DifferentiableAt.inner, IntervalIntegrable.absolutelyContinuousOnInterval_intervalIntegral, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, MeasureTheory.hasFDerivAt_convolution_right_with_param, ProbabilityTheory.IsGaussian.charFun_eq', ProbabilityTheory.covarianceBilinDual_eq_covariance, Matrix.PosSemidef.eq_sqrt_iff_sq_eq, signedDist_zero, AffineSubspace.signedInfDist_eq_signedDist_orthogonalProjection, EulerSine.sin_pi_mul_eq, integral_exp_Iic, Chebyshev.primeCounting_eq_theta_div_log_add_integral, NumberField.mixedEmbedding.span_idealLatticeBasis, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, InformationTheory.integral_llr_add_sub_measure_univ_nonneg, MeasureTheory.Integrable.integral_norm_prod_left, HasCompactSupport.hasFDerivAt_convolution_right, frontier_range_modelWithCornersEuclideanHalfSpace, SchwartzMap.integral_bilinear_deriv_right_eq_neg_left, MeasureTheory.condExp_stronglyMeasurable_simpleFunc_mul, ProbabilityTheory.covarianceBilinDual_zero, contDiff_bernoulliFun, HasFDerivWithinAt.inner, EuclideanSpace.instIsManifoldSphere, MeasureTheory.tendsto_sum_indicator_atTop_iff, Orientation.abs_volumeForm_apply_of_pairwise_orthogonal, circleAverage_log_norm_sub_constβ, ProbabilityTheory.condIndepSet_iff, MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul_of_measurable, ProbabilityTheory.differentiableOn_mgf, contDiffOn_abs, MeasureTheory.Integrable.integral_norm_condExpKernel, SmoothBumpFunction.contMDiffAt, ProbabilityTheory.complexMGF_id_mul_I, Real.one_div_sub_hasFPowerSeriesOnBall_zero, ContDiff.euclidean_dist, MeasureTheory.condExp_mul_of_aestronglyMeasurable_left, MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_det_fderiv_mul, Bundle.ContMDiffRiemannianMetric.pos, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_cgf', signedDist_triangle_left, IsContMDiffRiemannianBundle.exists_contMDiff, sum_Ico_le_integral_of_le, integral_sin_pow_mul_cos_pow_odd, integral_rpow_mul_exp_neg_mul_rpow, SmoothBumpCovering.sum_toSmoothPartitionOfUnity_eq, ProbabilityTheory.integral_gaussianPDFReal_eq_one, contMDiff_subtype_coe_Icc, ProperCone.innerDual_singleton, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_eq, InformationTheory.integral_klFun_rnDeriv, differentiable_inner, intervalIntegral.abs_integral_mono_interval, hasFDerivAt_integral_of_dominated_loc_of_lip', integral_id, ExistsContDiffBumpBase.u_int_pos, Real.differentiableAt_Gamma, Real.pow_mul_norm_iteratedFDeriv_fourier_le, NumberField.mixedEmbedding.mem_span_latticeBasis, ProbabilityTheory.evariance_eq_lintegral_ofReal, ProbabilityTheory.integral_condVar_add_variance_condExp, ContDiffWithinAt.norm_sq, Function.hasTemperateGrowth_norm_sq, ProbabilityTheory.analyticOn_cgf, Real.zero_at_infty_fourierIntegral, ProbabilityTheory.covarianceBilin_comm, intervalIntegral.integral_congr_codiscreteWithin, ProbabilityTheory.Kernel.tendsto_integral_density_of_monotone, InformationTheory.klDiv_of_ac_of_integrable, gradient_eq_deriv', MeasureTheory.L2.integral_inner_eq_sq_eLpNorm, MonotoneOn.intervalIntegrable_slope, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, SchwartzMap.smulRightCLM_apply_apply, Real.differentiableOn_Gamma_Ioi, ProbabilityTheory.analyticAt_cgf, InformationTheory.klDiv_def, MeasureTheory.L2.inner_indicatorConstLp_one, abs_wInner_le, NumberField.mixedEmbedding.negAt_apply_isReal_and_notMem, fderiv_norm_smul_neg, ExistsContDiffBumpBase.u_exists, Real.fourierIntegral_real_eq_integral_exp_smul, Real.deriv_fourierIntegral, NumberField.Units.dirichletUnitTheorem.unitLattice_span_eq_top, intervalIntegral.integral_eq_zero_iff_of_le_of_nonneg_ae, dense_differentiableAt_norm, AntitoneOn.sum_le_integral_Ico, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_eq, intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae, ContDiff.norm_sq, MonotoneOn.intervalIntegral_deriv_mem_uIcc, NumberField.mixedEmbedding.volume_preserving_negAt, Affine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint, SmoothPartitionOfUnity.sum_eq_one', integral_sin_mul_cosβ, MeasureTheory.Measure.withDensityα΅₯_absolutelyContinuous, ProbabilityTheory.iCondIndepSets_singleton_iff, NumberField.mixedEmbedding.negAt_apply_isComplex, Real.integral_rpowIntegrandββ_one_pos, ProbabilityTheory.hasFiniteIntegral_compProd_iff', ProbabilityTheory.integral_truncation_eq_intervalIntegral_of_nonneg, integral_sin_pow_aux, integral_comp_abs, ProbabilityTheory.setIntegral_stieltjesOfMeasurableRat, integral_div_sq_add_sq, SmoothPartitionOfUnity.mem_finsupport, Real.Wallis.W_eq_integral_sin_pow_div_integral_sin_pow, IsOpen.exists_contMDiff_support_eq, ProbabilityTheory.IndepFun.integral_fun_mul_eq_mul_integral, Matrix.instNonnegSpectrumClass, NumberField.mixedEmbedding.normAtComplexPlaces_normAtAllPlaces, DifferentiableAt.norm_sq, ProbabilityTheory.sum_variance_truncation_le, Orientation.areaForm'_apply, MeasureTheory.condExp_stronglyMeasurable_mul_of_bound, signedDist_smul_of_pos, IsContinuousRiemannianBundle.exists_continuous, MonotoneOn.sum_le_integral_Ico, ProbabilityTheory.condExp_set_generateFrom_singleton, intervalIntegral.integral_hasStrictFDerivAt, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, signedDist_lineMap_lineMap, mfderiv_coe_sphere_injective, ProbabilityTheory.variance_eq_sub, NumberField.mixedEmbedding.mem_negAt_plusPart_of_mem, NumberField.Units.regOfFamily_of_isMaxRank, intervalIntegral.inv_mul_integral_comp_add_div, analyticAt_sigmoid, contDiffAt_norm, tendsto_integral_mul_one_add_inv_smul_sq_pow, AnalyticOnNhd.circleAverage_log_norm_of_ne_zero, AffineSubspace.abs_signedInfDist_eq_dist_of_mem_affineSpan_insert, PiLp.volume_preserving_ofLp, integral_sin_pow_even_mul_cos_pow_even, ProbabilityTheory.Kernel.setIntegral_density_of_measurableSet, signedDist_vadd_left_swap, MeasureTheory.integrable_prod_iff, sum_mul_Ico_le_integral_of_monotone_antitone, HasFDerivWithinAt.norm_sq, ProbabilityTheory.meas_ge_le_variance_div_sq, differentiableAt_abs_neg, ProbabilityTheory.isGaussian_gaussianReal, norm_fderiv_norm_rpow_le, integral_inner, deriv_abs_zero, VectorFourier.fderiv_fourierIntegral, InnerProductGeometry.norm_ofLp_crossProduct, hasStrictDerivAt_abs, Bundle.RiemannianMetric.symm, MeasureTheory.integral_charFun_Icc, ProbabilityTheory.Kernel.tendsto_integral_density_of_antitone, ContDiffWithinAt.dist, ProbabilityTheory.moment_truncation_eq_intervalIntegral_of_nonneg, AffineSubspace.signedInfDist_eq_const_of_mem, MeasureTheory.mul_le_integral_rnDeriv_of_ac, intervalIntegral.inv_mul_integral_comp_sub_div, Function.Periodic.tendsto_atBot_intervalIntegral_of_pos', NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, DifferentiableOn.norm_sq, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_mem_fundamentalCone_iff, Differentiable.norm_rpow, intervalIntegral.integral_mono_ae, ProbabilityTheory.variance_continuousLinearMap_gaussianReal, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, ProbabilityTheory.covariance_eq_sub, MeasureTheory.integrable_conv_iff, signedDist_vadd_right, hasSum_sq_fourierCoeffOn, Real.circleAverage_mono_on_of_le_circle, ProbabilityTheory.strong_law_aux6, MeasureTheory.tendsto_sum_indicator_atTop_iff', MeasureTheory.integral_prod_mul, contDiff_norm_sq, tendsto_integral_mulExpNegMulSq_comp, SmoothBumpCovering.embeddingPiTangent_injective_mfderiv, intervalAverage_congr_codiscreteWithin, Polynomial.logMahlerMeasure_def, deriv_abs_pos, ProbabilityTheory.hasFPowerSeriesAt_mgf, Complex.integral_exp_neg_mul_rpow, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMap, MeasureTheory.Measure.integrable_compProd_iff, ContDiff.inner, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae, ProbabilityTheory.covarianceBilin_self_nonneg, HasDerivAt.norm_sq, ProbabilityTheory.integral_linearMap_gaussianReal, MeasureTheory.Measure.exists_integral_isMulLeftInvariant_eq_smul_of_hasCompactSupport, exists_msmooth_support_eq_eq_one_iff, Polynomial.Chebyshev.integral_eval_T_real_measureT_zero, MeasureTheory.integral_le_liminf_integral_of_forall_isOpen_measure_le_liminf_measure, MeasureTheory.L2.real_inner_indicatorConstLp_one_indicatorConstLp_one, ProbabilityTheory.condIndepSets_iff, integral_inv_of_neg, ProbabilityTheory.covarianceBilinDual_self_eq_variance, ProbabilityTheory.iCondIndepSet_iff, MeasureTheory.integral_condExpL2_eq_of_fin_meas_real, Orientation.areaForm_comp_linearIsometryEquiv, hasStrictFDerivAt_norm_sq, SmoothPartitionOfUnity.coe_finsupport, ConcaveOn.le_map_integral, Emetric.exists_contMDiffMap_forall_closedBall_subset, ProbabilityTheory.differentiableAt_iteratedDeriv_mgf, ProbabilityTheory.condVar_ae_le_condExp_sq, MDifferentiableOn.inner_bundle, ProbabilityTheory.Kernel.setIntegral_densityProcess, differentiableAt_norm_smul, AntitoneOn.integral_le_sum_Ico, MeasureTheory.setIntegral_abs_condExp_le, Metric.exists_contMDiffMap_forall_closedBall_subset, ProbabilityTheory.IndepFun.integral_fun_comp_mul_comp, Differentiable.norm_sq, exists_msmooth_zero_iff_one_iff_of_isClosed, ConcaveOn.set_average_mem_hypograph, norm_wInner_le, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul_real, ProbabilityTheory.covarianceBilinDual_self_nonneg, IccLeftChart_extend_bot, NumberField.mixedEmbedding.stdBasis_apply_isComplex_fst, ContDiffBump.measure_closedBall_le_integral, ProbabilityTheory.Kernel.integral_densityProcess, MeasureTheory.Integrable.integral_eq_integral_meas_le, SmoothPartitionOfUnity.finsum_smul_mem_convex, intervalIntegral.mul_integral_comp_add_mul, signedDist_lineMap_left, ProbabilityTheory.covarianceBilin_real_self, MeasureTheory.BoundedContinuousFunction.integral_eq_integral_meas_le, integral_univ_inv_one_add_sq, MeasureTheory.Integrable.integral_norm_compProd, NumberField.mixedEmbedding.fundamentalDomain_stdBasis, SmoothPartitionOfUnity.sum_le_one', ValueDistribution.characteristic_sub_characteristic_inv, NumberField.mixedEmbedding.span_latticeBasis, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, integral_exp_neg_rpow, AnalyticWithinAt.re_ofReal, Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay, InformationTheory.klDiv_eq_integral_klFun, VectorFourier.fourierSMulRight_apply, MeasureTheory.Integrable.integral_eq_integral_meas_lt, MeasureTheory.tendsto_ae_condExp, ProbabilityTheory.evariance_def', MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, integral_inv, SmoothBumpCovering.embeddingPiTangent_ker_mfderiv, ContMDiffOn.inner_bundle, SmoothPartitionOfUnity.sum_nonneg, intervalIntegral.abs_integral_le_integral_abs, Manifold.riemannianEDist_def, Real.one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae', signedDist_anticomm, NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mul, Orientation.areaForm_comp_rightAngleRotation, modelWithCornersEuclideanHalfSpace_zero, Matrix.PosSemidef.isUnit_sqrt_iff, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real, ProbabilityTheory.exponentialCDFReal_eq_integral, differentiableWithinAt_abs_neg, ContDiffAt.norm_sq, ProbabilityTheory.iteratedDeriv_mgf_zero, ProbabilityTheory.moment_truncation_eq_intervalIntegral, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, ProbabilityTheory.cdf_expMeasure_eq_integral, ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup, MeasureTheory.rnDeriv_ae_eq_condExp, NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlaces, MeasureTheory.Measure.haarScalarFactor_eq_integral_div, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, ProbabilityTheory.hasFiniteIntegral_comp_iff', ProbabilityTheory.covarianceOperator_inner, mellin_eq_fourierIntegral, hasStrictDerivAt_abs_neg, MDifferentiableWithinAt.inner_bundle, Orientation.inner_rightAngleRotation_left, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, integral_cos_pow_three, HasFDerivAt.inner, ProbabilityTheory.paretoCDFReal_eq_integral, SmoothBumpCovering.exists_finset_toSmoothPartitionOfUnity_eventuallyEq, integral_one_div_of_pos, ProbabilityTheory.covarianceBilin_apply_pi, ProbabilityTheory.deriv_mgf, ExistsContDiffBumpBase.u_smooth, intervalIntegral.intervalIntegral_pos_of_pos_on, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral', ProbabilityTheory.condExpKernel_ae_eq_condExp, signedDist_triangle_right, ProbabilityTheory.hasFiniteIntegral_comp_iff, contMDiffWithinAt_comp_projIcc_iff, Orientation.inner_mul_areaForm_sub', hasFDerivAt_polarCoord_symm, MeasureTheory.dist_convolution_le', AnalyticWithinAt.im_ofReal, ProbabilityTheory.HasGaussianLaw.charFun_map_eq, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, abs_signedDist_eq_dist_iff_vsub_mem_span, Real.iteratedDeriv_fourier, ProbabilityTheory.Kernel.integral_density, Real.eulerMascheroniConstant_eq_neg_deriv, EuclideanSpace.volume_ball_fin_three, ProbabilityTheory.IsGaussian.integral_dual, Orientation.abs_areaForm_le, IsOpen.exists_msmooth_support_eq_aux, integral_log_sin_zero_pi, Polynomial.Chebyshev.integral_eval_T_real_mul_eval_T_real_measureT, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMapBasis, intervalIntegral.integral_pos_iff_support_of_nonneg_ae, MeasureTheory.L2.inner_indicatorConstLp_eq_setIntegral_inner, MeasureTheory.Integrable.integral_norm_condDistrib, NumberField.mixedEmbedding.euclidean.instIsZLatticeRealMixedSpaceIntegerLattice, signedDist_neg, ProbabilityTheory.covarianceBilin_apply_basisFun, exists_contMDiff_zero_iff_one_iff_of_isClosed, ProbabilityTheory.condExpKernel_ae_eq_trim_condExp, integral_inv_sq_add_sq, NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single, ProbabilityTheory.setIntegral_preCDF_fst, NumberField.mixedEmbedding.negAt_symm, VectorFourier.contDiff_fourierIntegral, ConcaveOn.le_map_average, ProbabilityTheory.integrable_compProd_iff, intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left, Polynomial.sum_sq_norm_coeff_eq_circleAverage, ContDiffBump.contDiff_normed, integral_rpow, AnalyticAt.harmonicAt_re, ProbabilityTheory.iCondIndepSets_iff, Diffeology.isPlot_iff_contDiff, Matrix.PosSemidef.sq_sqrt, signedDist_vsub_self_rev, InformationTheory.toReal_klDiv_of_measure_eq, intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae, contDiffAt_inner, NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, OrthonormalBasis.measurePreserving_repr_symm, NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIntegerLattice, MeasureTheory.measureReal_abs_gt_le_integral_charFun, DifferentiableOn.inner, integral_exp_neg_Ioi, Differentiable.inner, signedDist_linear_apply, NumberField.mixedEmbedding.negAt_apply_isReal_and_mem, oneTangentSpaceIcc_def, Real.abs_circleAverage_le_circleAverage_abs, IccRightChart_extend_top_mem_frontier, NumberField.mixedEmbedding.volume_negAt_plusPart, ProbabilityTheory.integral_truncation_le_integral_of_nonneg, SmoothPartitionOfUnity.sum_eq_one, SchwartzMap.hasDerivAt, MeasureTheory.tendsto_eLpNorm_condExp, MeasureTheory.eLpNorm_one_condExp_le_eLpNorm, integral_log, signedDist_self, integral_sqrt_one_sub_sq, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_measure_nhdsWithin_pos, circleAverage_log_norm_add_const_eq_posLog, Real.Gamma_eq_integral, signedDist_vsub_self, MeasureTheory.SignedMeasure.rnDeriv_smul, Affine.Simplex.exists_forall_signedInfDist_eq_iff_eq_incenter, signedDist_smul, MeromorphicOn.circleAverage_log_norm, ZLattice.volume_image_eq_volume_div_covolume, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul, ContDiffOn.norm_sq, Real.map_linearMap_volume_pi_eq_smul_volume_pi, intervalIntegral.inv_mul_integral_comp_div_sub, Euclidean.closedBall_eq_preimage, NumberField.mixedEmbedding.iUnion_negAt_plusPart_union, Matrix.PosSemidef.inv_sqrt, intervalIntegral.differentiable_integral_of_continuous, integral_log_from_zero_of_pos, LipschitzWith.locallyIntegrable_lineDeriv, SmoothBumpCovering.embeddingPiTangent_injOn, EulerSine.integral_cos_pow_eq, intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le, ConvexOn.average_mem_epigraph, MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaar, MeasureTheory.integral_condExp_indicator, Function.locallyFinsuppWithin.logCounting_divisor_eq_circleAverage_sub_const, Orientation.abs_areaForm_of_orthogonal, ProbabilityTheory.Kernel.tendsto_setIntegral_densityProcess, LipschitzOnWith.ae_differentiableWithinAt_real, MeasureTheory.AEStronglyMeasurable.ae_integrable_condDistrib_map_iff, integral_sin, Function.hasTemperateGrowth_inner_left, exists_eq_const_mul_intervalIntegral_of_ae_nonneg, ProbabilityTheory.hasDerivAt_iteratedDeriv_mgf, Real.le_integral_rpowIntegrandββ_one, ContinuousLinearMap.intervalIntegral_apply, analyticWithinAt_sigmoid, ProbabilityTheory.variance_le_expectation_sq, MeasureTheory.Integrable.withDensityα΅₯_trim_eq_integral, analyticOn_sigmoid, EuclideanSpace.volume_preserving_symm_measurableEquiv_toLp, MeasureTheory.integral_fin_nat_prod_eq_prod, MeasureTheory.Measure.integral_isMulLeftInvariant_eq_smul_of_hasCompactSupport, ContDiffBump.integral_le_measure_closedBall, mdifferentiableWithinAt_comp_projIcc_iff, Real.zero_at_infty_fourier, Orientation.inner_sq_add_areaForm_sq, intervalIntegral.integral_nonneg_of_ae_restrict, signedDist_smul_of_neg, nnnorm_fderiv_norm_rpow_le, Real.hasFPowerSeriesOnBall_linear_zero, differentiableAt_abs_pos, Polynomial.Chebyshev.integral_eval_T_real_measureT_of_ne_zero, Real.hasDerivAt_Gamma_one_half, ProbabilityTheory.isPosSemidef_covarianceBilinDual, fderiv_norm_smul, Diffeology.IsContDiffCompatible.isPlot_iff, MeasureTheory.Measure.integrable_integral_norm_of_integrable_comp, NumberField.mixedEmbedding.injective_mixedSpaceOfRealSpace, range_mfderiv_coe_sphere, ProbabilityTheory.strong_law_aux7, MeasureTheory.integrable_prod_iff', Affine.Simplex.sign_signedInfDist_touchpoint_empty, MeasureTheory.SignedMeasure.singularPart_add_withDensity_rnDeriv_eq, Real.one_add_rpow_hasFPowerSeriesAt_zero, integral_sin_pow_odd_mul_cos_pow, signedDist_vadd_right_swap, ProbabilityTheory.integral_condCDF, ValueDistribution.proximity_zero_of_complexValued, SchwartzMap.integralCLM_apply, EulerSine.tendsto_integral_cos_pow_mul_div, MeasureTheory.withDensityα΅₯_toReal, ProbabilityTheory.Kernel.condExp_densityProcess, EuclideanSpace.volume_ball_fin_two, EuclideanSpace.inner_basisFun_real, iccLeftChart_extend_zero, SmoothBumpCovering.comp_embeddingPiTangent_mfderiv, MeasureTheory.SignedMeasure.singularPart_smul_nnreal, ProbabilityTheory.covarianceBilin_real, bernoulliFun_eq_integral, ProbabilityTheory.moment_def, Euclidean.ball_eq_preimage, InformationTheory.rightDeriv_klFun_one, hasDerivAt_abs, NumberField.mixedEmbedding.stdBasis_apply_isReal, Function.RCLike.hasTemperateGrowth_ofReal, EuclideanSpace.volume_ball, ContDiffAt.norm, intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae, ProbabilityTheory.covarianceBilin_of_not_memLp, InformationTheory.rightDeriv_klFun, interior_range_modelWithCornersEuclideanHalfSpace, ExistsContDiffBumpBase.y_smooth, contDiff_inner, ProbabilityTheory.condVar_bot', Real.hasDerivAt_Gamma_one, IntervalIntegrable.intervalIntegrable_slope, ConvexOn.map_integral_le, Differentiable.dist, ProbabilityTheory.condVar_of_sigmaFinite, ContDiffAt.dist, innerSL_real_flip, tsum_sq_fourierCoeffOn, ProbabilityTheory.covarianceBilinDual_comm, ProbabilityTheory.iteratedDeriv_two_cgf, SchwartzMap.integral_smul_lineDerivOp_right_eq_neg_left, integral_exp_mul_Ioi, integral_sin_mul_cos_sq, SmoothPartitionOfUnity.exists_pos_of_mem, ProbabilityTheory.deriv_mgf_zero, Real.deriv_sigmoid, one_add_rpow_hasFPowerSeriesAt_zero, ProbabilityTheory.iCondIndepFun_iff, circleAverage_log_norm_sub_const_eq_posLog, Orientation.volumeForm_robust', exists_smooth_zero_one_of_isClosed, NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIdealLattice, ContMDiff.inner_bundle, analyticAt_log, MeasureTheory.ae_mem_limsup_atTop_iff, signedDist_vadd_left, Diffeology.IsPlot.contDiff, ContDiffBump.convolution_eq_right, ExistsContDiffBumpBase.w_def, ProbabilityTheory.deriv_cgf, isBoundedBilinearMap_inner, intervalIntegral.integral_hasFDerivWithinAt, circleAverage_log_norm_factorizedRational, SmoothBumpCovering.embeddingPiTangent_injective, ContDiff.dist, ProbabilityTheory.covarianceBilin_apply, exists_contMDiff_support_eq_eq_one_iff, volume_regionBetween_eq_integral', MeasureTheory.ae_bdd_condExp_of_ae_bdd, hasDerivAt_norm_rpow, ContMDiffAt.inner_bundle, NumberField.mixedEmbedding.latticeBasis_apply, SmoothPartitionOfUnity.sum_finsupport_smul_eq_finsum, ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp, signedDist_apply_linear_apply, SchwartzMap.integral_mul_deriv_eq_neg_deriv_mul, AnalyticAt.harmonicAt_log_norm, ProbabilityTheory.HasGaussianLaw.charFunDual_map_eq_fun, MonotoneOn.exists_tendsto_deriv_liminf_lintegral_enorm_le, ProbabilityTheory.covarianceBilin_map, AffineSubspace.signedInfDist_singleton, intervalIntegral.mul_integral_comp_mul_add, Bundle.ContinuousRiemannianMetric.pos, ProbabilityTheory.strong_law_aux4, SchwartzMap.derivCLM_apply, ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup_atTop, Real.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, IsCoercive.continuousLinearEquivOfBilin_apply, intervalIntegral.integral_nonneg_of_ae, Orientation.volumeForm_zero_neg, SmoothPartitionOfUnity.contMDiff_finsum_smul, ContDiffBump.dist_normed_convolution_le, SmoothPartitionOfUnity.sum_finsupport, Orientation.areaForm_map, deriv_bernoulliFun, det_fderivPiPolarCoordSymm, ProbabilityTheory.condVar_bot_ae_eq, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, NumberField.mixedEmbedding.commMap_apply_of_isReal, Fourier.norm_fourierIntegral_le_integral_norm, ZSpan.fundamentalDomain_pi_basisFun, LipschitzWith.ae_differentiableAt_of_real, MeasureTheory.Measure.integrable_comp_iff, Bundle.RiemannianMetric.pos, IsOpen.exists_contDiff_support_eq, integral_zpow, exists_eq_interval_average_of_measure, NumberField.mixedEmbedding.hasFDerivAt_polarCoordReal_symm, Function.Complex.hasTemperateGrowth_ofReal, ConvexOn.map_average_le, ProbabilityTheory.analyticOnNhd_mgf, integral_one_div_one_add_sq, MeasureTheory.BoundedContinuousFunction.integral_le_of_levyProkhorovEDist_lt, integral_one, circleAverage_log_norm_sub_constβ, Manifold.pathELength_eq_lintegral_mfderiv_Icc, MeasureTheory.hasFiniteIntegral_prod_iff, MeasureTheory.charFun_map_mul, Orientation.inner_rightAngleRotationAuxβ_right, hasFDerivAt_pi_polarCoord_symm, ContDiffWithinAt.inner, NumberField.mixedEmbedding.latticeBasis_repr_apply, InformationTheory.not_differentiableWithinAt_klFun_Ioi_zero, DifferentiableWithinAt.norm_sq, Real.fourierIntegral_continuousLinearMap_apply', integral_sin_pow_succ_le, ProbabilityTheory.iteratedDeriv_two_cgf_eq_integral, signedDist_right_lineMap, ProbabilityTheory.uncenteredCovarianceBilin_zero, Real.differentiable_fourierChar, hasFDerivAt_integral_of_dominated_of_fderiv_le, VectorFourier.fourierPowSMulRight_apply, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_cgf, SmoothBumpCovering.support_toSmoothPartitionOfUnity_subset, DifferentiableOn.dist, NumberField.mixedEmbedding.normAtPlace_negAt, Chebyshev.integral_theta_div_log_sq_isBigO, AlternatingMap.measure_def, Real.tendsto_Icc_vitaliFamily_left, integral_le_sum_Ico_of_le, integral_gaussian, Orientation.areaForm_map_complex, intervalIntegral.integral_smul_const, intervalIntegral.mul_integral_comp_sub_mul, contMDiffOn_comp_projIcc_iff, intervalIntegral.abs_integral_eq_abs_integral_uIoc, NumberField.mixedEmbedding.finrank, integral_one_div, ProbabilityTheory.integral_id_gaussianReal, ProbabilityTheory.meas_ge_le_evariance_div_sq, SmoothBumpFunction.contMDiff, AnalyticAt.re_ofReal, Affine.Simplex.abs_signedInfDist_eq_dist_of_mem_affineSpan_range, Orientation.inner_rightAngleRotation_right, volume_euclideanSpace_eq_dirac, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, MeasureTheory.Measure.exists_integral_isAddLeftInvariant_eq_smul_of_hasCompactSupport, ConcaveOn.average_mem_hypograph, integral_sin_sq_mul_cos, ProbabilityTheory.IsRatCondKernelCDFAux.setIntegral_iInf_rat_gt, intervalIntegral.norm_integral_le_integral_norm, Affine.Simplex.ExcenterExists.signedInfDist_excenter, Orientation.volumeForm_apply_le, BoxIntegral.Box.volume_apply, SmoothPartitionOfUnity.finite_tsupport, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral, Complex.integral_rpow_mul_exp_neg_mul_rpow, NumberField.mixedEmbedding.negAt_apply_norm_isReal, Chebyshev.integral_theta_div_log_sq_isLittleO, EulerSine.integral_cos_pow_pos, MonotoneOn.integral_le_sum, MeasureTheory.pdf.IsUniform.integral_eq, ContDiff.norm, AntitoneOn.sum_le_integral, integral_pow_mul_le_of_le_of_pow_mul_le, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, hasDerivWithinAt_abs_neg, StieltjesFunction.ae_hasDerivAt, contDiffWithinAt_abs, hasSum_sq_fourierCoeff, ProbabilityTheory.strong_law_aux1, ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup_atBot, Orientation.kahler_apply_apply, Orientation.inner_rightAngleRotationAuxβ_left, exists_embedding_euclidean_of_compact, HasDerivAt.inner, Orientation.areaForm_apply_self, ProbabilityTheory.hasFiniteIntegral_compProd_iff, Real.differentiable_fourierChar_neg_bilinear_right, ProbabilityTheory.variance_linearMap_gaussianReal, MeasureTheory.condExp_stronglyMeasurable_mul_of_boundβ, AffineSubspace.signedInfDist_def, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply, ValueDistribution.logCounting_zero_sub_logCounting_top_eq_circleAverage_sub_const, MeasureTheory.BoundedContinuousFunction.inner_toLp, MeasureTheory.integral_fintype_prod_volume_eq_prod, ProbabilityTheory.IsGaussian.integral_dual_conv_map_neg_eq_zero, signedDist_lineMap_right, MeasureTheory.Integrable.uniformIntegrable_condExp_filtration, Real.integral_rpow_mul_exp_neg_mul_Ioi, SchwartzMap.tsupport_derivCLM_subset, Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIcc, SchwartzMap.integral_smul_laplacian_right_eq_left, SchwartzMap.le_seminorm', differentiable_norm_rpow, VectorFourier.fourierIntegral_probChar, Affine.Simplex.sign_signedInfDist_incenter, Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter, ProbabilityTheory.evariance_eq_zero_iff, integral_inv_one_add_sq, VectorFourier.norm_fourierSMulRight_le, AlternatingMap.measure_parallelepiped, ProbabilityTheory.Kernel.setIntegral_density, Affine.Simplex.signedInfDist_affineCombination, NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis, ProbabilityTheory.strong_law_aux2, intervalIntegral.mul_integral_comp_mul_right, Real.one_div_sub_pow_hasFPowerSeriesOnBall_zero, signedDist_apply, intervalIntegral.norm_integral_le_abs_integral_norm, UnitAddTorus.hasSum_sq_mFourierCoeff, Polynomial.Chebyshev.integral_eval_T_real_mul_eval_T_real_measureT_of_ne, integral_sin_pow_odd, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp_real, signedDist_eq_dist_iff_vsub_mem_span, volume_regionBetween_eq_integral, VectorFourier.norm_fourierPowSMulRight_le, SmoothPartitionOfUnity.mem_fintsupport_iff, Emetric.exists_smooth_forall_closedBall_subset, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, Real.hasFDerivAt_fourierChar_neg_bilinear_right, intervalIntegral.inv_mul_integral_comp_div, ProbabilityTheory.strong_law_aux3, MeasureTheory.BoundedContinuousFunction.integral_eq_integral_meas_le_of_hasFiniteIntegral, VectorFourier.norm_fourierSMulRight, Function.Periodic.integral_le_sSup_add_zsmul_of_pos, differentiableOn_abs, ProbabilityTheory.hasDerivAt_mgf, InnerProductSpace.laplacian_eq_iteratedDeriv_real, intervalIntegral.integral_eq_zero_iff_of_nonneg_ae, ProbabilityTheory.strong_law_ae_real, Real.iteratedDeriv_fourierIntegral, ContDiffAt.inner, ExistsContDiffBumpBase.w_integral, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, ProbabilityTheory.deriv_cgf_zero, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul, NumberField.mixedEmbedding.euclidean.finrank, DifferentiableAt.norm, Real.differentiable_fourierChar_neg_bilinear_left, fderiv_norm_smul_pos, integral_Ioi_inv_one_add_sq, Real.circleAverage_mono, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symm, Affine.Simplex.ExcenterExists.signedInfDist_excenter_eq_mul_sum_inv, MeasureTheory.Measure.integral_isAddLeftInvariant_isAddRightInvariant_combo, Polynomial.Chebyshev.integral_eval_T_real_mul_self_measureT_zero, NumberField.mixedEmbedding.measurableSet_negAt_plusPart, range_modelWithCornersEuclideanHalfSpace, VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, ProbabilityTheory.iIndepFun.integral_fun_prod_comp, integral_exp_neg_Ioi_zero, Matrix.PosSemidef.sqrt_mul_self, Orientation.areaForm_rightAngleRotation_right, MDifferentiableAt.inner_bundle, contDiff_norm_rpow, exists_contDiff_tsupport_subset, ProbabilityTheory.indepFun_iff_integral_comp_mul, Affine.Simplex.exists_forall_signedInfDist_eq_iff_excenterExists_and_eq_excenter, tsum_sq_fourierCoeff, intervalIntegral.integral_pos, integral_sin_pow, ProbabilityTheory.iIndepFun.integral_prod_comp, AntitoneOn.integral_le_sum, integral_gaussian_Ioi, fderiv_norm_rpow, intervalIntegral_ofReal, Real.Icc_mem_vitaliFamily_at_right, ConcaveOn.le_map_set_average, Real.hasDerivAt_fourierIntegral, AnalyticOn.re_ofReal, AffineSubspace.signedInfDist_apply_self, integral_sin_sq_mul_cos_sq, ProbabilityTheory.covarianceBilinDual_of_not_memLp, integral_mul_rpow_one_add_sq, MeasureTheory.charFun_map_eq_charFunDual_smul, NumberField.mixedEmbedding.normAtAllPlaces_mixedSpaceOfRealSpace, ProbabilityTheory.condVar_ae_eq_condExp_sq_sub_sq_condExp, NumberField.mixedEmbedding.det_fderivPolarCoordRealSymm, abs_integral_sub_setIntegral_mulExpNegMulSq_comp_lt, ContMDiff.codRestrict_sphere, SchwartzMap.tsum_eq_tsum_fourierIntegral, ProbabilityTheory.uncenteredCovarianceBilinDual_apply, MeasureTheory.condExpIndSMul_ae_eq_smul, Quaternion.linearIsometryEquivTuple_apply, MeasureTheory.intervalIntegrable_charFun, integral_Iic_inv_one_add_sq, SmoothPartitionOfUnity.toPartitionOfUnity_toFun, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_integral_of_monotone, SmoothPartitionOfUnity.contMDiff_smul, ProbabilityTheory.condIndepFun_iff, TemperedDistribution.derivCLM_apply_apply, integral_cos_sq, abs_signedDist_le_dist, NumberField.mixedEmbedding.disjoint_span_commMap_ker, mfderiv_subtype_coe_Icc_one, Real.integral_rpowIntegrandββ_eq_rpow_mul_const, intervalIntegral.integral_hasFDerivAt, ValueDistribution.proximity_coe, MeasureTheory.tendsto_iff_forall_lipschitz_integral_tendsto, intervalIntegral.fderiv_integral, ProbabilityTheory.gaussianReal_apply_eq_integral, ProbabilityTheory.IsGaussian.charFunDual_eq', MeasureTheory.integral_prod_smul, ProbabilityTheory.condExp_eq_zero_or_one_of_condIndepSet_self, AffineSubspace.signedInfDist_apply_of_mem, ProbabilityTheory.IsRatCondKernelCDFAux.setIntegral, Real.hasDerivAt_Gamma_nat, HasStrictFDerivAt.inner, MeasureTheory.ContinuousMap.inner_toLp, differentiableAt_abs, ProbabilityTheory.setIntegral_stieltjesOfMeasurableRat_rat, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul', intervalIntegral.norm_integral_le_abs_of_norm_le, ProbabilityTheory.analyticAt_iteratedDeriv_mgf, ProbabilityTheory.charFun_gaussianReal, exists_eq_interval_average, exists_smooth_zero_one_nhds_of_isClosed, DifferentiableOn.norm, integral_exp_Iic_zero, ContDiffOn.norm, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, signedDist_apply_linear, Bundle.RiemannianMetric.continuousAt, parallelepiped_orthonormalBasis_one_dim, integral_log_from_zero, MeasureTheory.integrable_mconv_iff, VectorFourier.norm_fourierIntegral_le_integral_norm, Manifold.exists_lt_of_riemannianEDist_lt, MeasureTheory.integral_abs_condExp_le, StrictConvexOn.ae_eq_const_or_map_average_lt, VectorFourier.hasFDerivAt_fourierChar_smul, OrthonormalBasis.measurePreserving_measurableEquiv, Real.fourierIntegral_real_eq, InformationTheory.not_differentiableAt_klFun_zero, MeasureTheory.measure_unitBall_eq_integral_div_gamma, integral_cos_sq_sub_sin_sq, ProbabilityTheory.variance_tilted_mul, MeasureTheory.le_integral_rnDeriv_of_ac, SmoothBumpCovering.embeddingPiTangent_coe, SchwartzMap.integral_smul_deriv_right_eq_neg_left, SmoothPartitionOfUnity.nonneg', ProbabilityTheory.covarianceBilinDual_of_not_memLp', Function.hasTemperateGrowth_one_add_norm_sq_rpow, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_continuousOn, ContDiffWithinAt.norm, SmoothPartitionOfUnity.IsSubordinate.contMDiff_finsum_smul, AbsolutelyContinuousOnInterval.integral_mul_deriv_eq_deriv_mul, ProbabilityTheory.analyticOn_iteratedDeriv_mgf, MeasureTheory.Integrable.integral_norm_condKernel, intervalIntegral.inv_mul_integral_comp_div_add, Orientation.volumeForm_comp_linearIsometryEquiv, norm_fderiv_norm_id_rpow, NumberField.Units.basisOfIsMaxRank_fundSystem, NumberField.mixedEmbedding.fundamentalCone.linearIndependent_completeFamily, intervalIntegral.norm_integral_le_integral_norm_uIoc, NumberField.mixedEmbedding.commMap_canonical_eq_mixed, Affine.Simplex.signedInfDist_apply_of_ne, exists_contMDiffMap_one_nhds_of_subset_interior, signedDist_left_lineMap, DifferentiableWithinAt.inner, NumberField.mixedEmbedding.norm_negAt, SmoothPartitionOfUnity.sum_le_one, VectorFourier.fourierIntegral_fderiv, ProbabilityTheory.HasCondSubgaussianMGF.ae_trim_condExp_le, IccRightChart_extend_top, integral_one_div_of_neg, ContDiffBump.convolution_tendsto_right_of_continuous, fderivInnerCLM_apply, intervalIntegral.integral_lt_integral_of_ae_le_of_measure_setOf_lt_ne_zero, ContMDiffWithinAt.inner_bundle, ProbabilityTheory.HasGaussianLaw.charFunDual_map_eq, MeasureTheory.Integrable.integral_eq_integral_Ioc_meas_le, boundary_Icc, MeasureTheory.tendsto_integral_meas_thickening_le, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, Real.fderiv_fourierChar_neg_bilinear_left_apply, Real.exists_measure_rpow_eq_integral, Real.fourierIntegral_continuousMultilinearMap_apply', ValueDistribution.proximity_top, ProbabilityTheory.integrable_comp_iff, MeasureTheory.lintegral_comp_eq_lintegral_meas_lt_mul, integral_sin_pow_antitone, Matrix.PosDef.posDef_sqrt, integral_pow_abs_sub_uIoc, Real.circleAverage_nonneg_of_nonneg, EuclideanSpace.volume_closedBall, intervalIntegral.integral_nonneg_of_forall, InformationTheory.deriv_klFun, one_add_rpow_hasFPowerSeriesOnBall_zero, AnalyticOnNhd.im_ofReal, boundary_product, Manifold.exists_lt_locally_constant_of_riemannianEDist_lt, differentiable_sigmoid, NumberField.mixedEmbedding.normAtPlace_mixedSpaceOfRealSpace, ProbabilityTheory.IsGaussian.eq_gaussianReal, Real.one_div_sub_sq_hasFPowerSeriesOnBall_zero, ProbabilityTheory.uncenteredCovarianceBilinDual_zero, ProbabilityTheory.integral_tilted_mul_self, integrableOn_Ioi_deriv_norm_ofReal_cpow, intervalIntegral.integral_mul_const, AbsolutelyContinuousOnInterval.intervalIntegrable_deriv, ProbabilityTheory.cdf_gammaMeasure_eq_integral, MeasureTheory.integral_comap_eq_mulEquivHaarChar_smul, fourier_gaussian_pi, Function.Periodic.tendsto_atTop_intervalIntegral_of_pos', not_differentiableAt_abs_zero, MonotoneOn.ae_differentiableWithinAt, ValueDistribution.proximity_sub_proximity_inv_eq_circleAverage, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, Orientation.areaForm_rightAngleRotation_left, Differentiable.norm, Real.deriv_fourier, contDiff_sigmoid, NumberField.mixedEmbedding.disjoint_negAt_plusPart, DifferentiableAt.dist, IccLeftChart_extend_bot_mem_frontier, fderiv_norm_sq_apply, LipschitzWith.ae_differentiableAt_real, NumberField.mixedEmbedding.volume_fundamentalDomain_stdBasis, Icc_isBoundaryPoint_top, integral_sin_pow_even, MeasureTheory.condExp_mul_of_stronglyMeasurable_left, fderiv_norm_sq, MeasureTheory.addEquivAddHaarChar_smul_integral_map, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', ContDiffOn.dist, MDifferentiable.inner_bundle, fourierIntegral_gaussian_pi', hasDerivAt_abs_pos, LipschitzWith.integral_lineDeriv_mul_eq, MeasureTheory.condExpL2_indicator_nonneg, HasCompactSupport.hasFDerivAt_convolution_left, instIsManifoldIcc, Bundle.ContinuousRiemannianMetric.isVonNBounded, Matrix.PosSemidef.sqrt_eq_iff_eq_sq, NumberField.mixedEmbedding.mem_rat_span_latticeBasis, ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc, Orientation.inner_mul_areaForm_sub, ProbabilityTheory.integral_preCDF_fst, fderiv_inner_apply, SmoothBumpCovering.toSmoothPartitionOfUnity_zero_of_zero, contDiffAt_abs, MeasureTheory.Integrable.uniformIntegrable_condExp, SmoothPartitionOfUnity.contMDiff_sum, contMDiffOn_projIcc, NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlaces, ContDiffBump.integral_pos, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, Metric.exists_contMDiffMap_forall_closedEBall_subset, BoxIntegral.unitPartition.tag_mem_smul_span, signedDist_vadd_vadd, parallelepiped_single, contMDiff_circleExp, SchwartzMap.tsum_eq_tsum_fourier, NumberField.mixedEmbedding.normAtAllPlaces_normAtAllPlaces, ProbabilityTheory.IndepFun.integral_mul_eq_mul_integral, hasFDerivAt_integral_of_dominated_loc_of_lip, intervalIntegral.norm_integral_le_of_norm_le, GaussianFourier.integral_rexp_neg_mul_sq_norm, Real.tendsto_Icc_vitaliFamily_right, intervalIntegral.differentiableOn_integral_of_continuous, differentiable_circleMap, AnalyticAt.im_ofReal, intervalIntegral.integral_nonneg, NumberField.mixedEmbedding.mixedSpaceOfRealSpace_apply, ProbabilityTheory.analyticOnNhd_iteratedDeriv_mgf, Orientation.abs_volumeForm_apply_le, intervalIntegral.mul_integral_comp_mul_left, Affine.Simplex.signedInfDist_incenter
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