RiemannLebesgueLemma

📁 Source: Mathlib/Analysis/Fourier/RiemannLebesgueLemma.lean

Statistics

Metric	Count
Definitions	0
Theorems tendsto_integral_exp_smul_cocompact, zero_at_infty_fourier, zero_at_infty_fourierIntegral, zero_at_infty_vector_fourierIntegral, fourierIntegral_eq_half_sub_half_period_translate, fourierIntegral_half_period_translate, tendsto_integral_exp_inner_smul_cocompact, tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_support, tendsto_integral_exp_smul_cocompact, tendsto_integral_exp_smul_cocompact_of_inner_product	10
Total	10

Real

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
tendsto_integral_exp_smul_cocompact 📖	mathematical	—	Filter.Tendsto Real MeasureTheory.integral NormedSpace.complexToReal NormedAddCommGroup.toSeminormedAddCommGroup MeasureTheory.MeasureSpace.toMeasurableSpace measureSpace MeasureTheory.MeasureSpace.volume Circle Circle.instSMul SMulZeroClass.toSMul Complex AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass ESeminormedAddMonoid.toAddMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ESeminormedAddCommMonoid.toESeminormedAddMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Complex.instSemiring Module.toDistribMulAction ESeminormedAddCommMonoid.toAddCommMonoid NormedSpace.toModule Complex.instNormedField DFunLike.coe AddChar instAddMonoid DivInvMonoid.toMonoid Group.toDivInvMonoid CommGroup.toGroup Circle.instCommGroup AddChar.instFunLike fourierChar instNeg instMul Filter.cocompact pseudoMetricSpace nhds NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedAddCommGroup.toAddCommGroup	—	mul_comm tendsto_integral_exp_inner_smul_cocompact borelSpace FiniteDimensional.rclike_to_real
zero_at_infty_fourier 📖	mathematical	—	Filter.Tendsto Real FourierTransform.fourier instFourierTransform normedAddCommGroup RCLike.toInnerProductSpaceReal instRCLike measurableSpace borelSpace FiniteDimensional.rclike_to_real Filter.cocompact UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace pseudoMetricSpace nhds SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedAddCommGroup.toAddCommGroup	—	tendsto_integral_exp_inner_smul_cocompact borelSpace FiniteDimensional.rclike_to_real
zero_at_infty_fourierIntegral 📖	mathematical	—	Filter.Tendsto Real FourierTransform.fourier instFourierTransform normedAddCommGroup RCLike.toInnerProductSpaceReal instRCLike measurableSpace borelSpace FiniteDimensional.rclike_to_real Filter.cocompact UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace pseudoMetricSpace nhds SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedAddCommGroup.toAddCommGroup	—	zero_at_infty_fourier
zero_at_infty_vector_fourierIntegral 📖	mathematical	—	Filter.Tendsto ContinuousLinearMap Real CommSemiring.toSemiring instCommSemiring RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace pseudoMetricSpace NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule VectorFourier.fourierIntegral commRing ContinuousLinearMap.addCommGroup instRing instAddCommGroup instIsTopologicalAddGroupReal ContinuousLinearMap.module Algebra.to_smulCommClass Algebra.id UniformContinuousConstSMul.to_continuousConstSMul Algebra.toSMul Ring.uniformContinuousConstSMul instIsUniformAddGroupReal IsTopologicalSemiring.toContinuousMul NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing IsTopologicalRing.toIsTopologicalSemiring instIsTopologicalRingReal IsTopologicalSemiring.toContinuousAdd NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing NonUnitalNormedCommRing.toNonUnitalCommRing NormedCommRing.toNonUnitalNormedCommRing normedCommRing fourierChar LinearMap.flip ContinuousLinearMap.addCommMonoid topDualPairing Filter.cocompact StrongDual semiring ContinuousLinearMap.topologicalSpace normedField nhds SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedAddCommGroup.toAddCommGroup	—	tendsto_integral_exp_smul_cocompact

(root)

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
fourierIntegral_eq_half_sub_half_period_translate 📖	mathematical	MeasureTheory.Integrable UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup SeminormedAddGroup.toContinuousENorm SeminormedAddCommGroup.toSeminormedAddGroup MeasureTheory.MeasureSpace.toMeasurableSpace measureSpaceOfInnerProductSpace MeasureTheory.MeasureSpace.volume	MeasureTheory.integral NormedSpace.complexToReal Circle Circle.instSMul SMulZeroClass.toSMul Complex AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass ESeminormedAddMonoid.toAddMonoid ESeminormedAddCommMonoid.toESeminormedAddMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Complex.instSemiring Module.toDistribMulAction ESeminormedAddCommMonoid.toAddCommMonoid NormedSpace.toModule Complex.instNormedField DFunLike.coe AddChar Real Real.instAddMonoid DivInvMonoid.toMonoid Group.toDivInvMonoid CommGroup.toGroup Circle.instCommGroup AddChar.instFunLike Real.fourierChar Real.instNeg Inner.inner InnerProductSpace.toInner Real.instRCLike DivInvMonoid.toDiv Complex.instDivInvMonoid Complex.instOne instOfNatAtLeastTwo Complex.instNatCast Nat.instAtLeastTwoHAddOfNat SubNegMonoid.toSub AddGroup.toSubNegMonoid NormedAddGroup.toAddGroup NormedAddCommGroup.toNormedAddGroup AddCommMagma.toAdd AddCommSemigroup.toAddCommMagma AddCommMonoid.toAddCommSemigroup	—	Nat.instAtLeastTwoHAddOfNat smul_sub MeasureTheory.integral_sub Real.fourierIntegral_convergent_iff MeasureTheory.Integrable.comp_add_right ContinuousAdd.measurableAdd IsTopologicalAddGroup.toContinuousAdd SeminormedAddCommGroup.toIsTopologicalAddGroup MeasureTheory.IsAddLeftInvariant.isAddRightInvariant MeasureTheory.Measure.IsAddHaarMeasure.toIsAddLeftInvariant instIsAddHaarMeasureVolume fourierIntegral_half_period_translate sub_eq_add_neg neg_neg two_smul smul_assoc IsScalarTower.left smul_eq_mul one_div inv_mul_cancel₀ Complex.instCharZero one_smul
fourierIntegral_half_period_translate 📖	mathematical	—	MeasureTheory.integral NormedSpace.complexToReal NormedAddCommGroup.toSeminormedAddCommGroup MeasureTheory.MeasureSpace.toMeasurableSpace measureSpaceOfInnerProductSpace MeasureTheory.MeasureSpace.volume Circle Circle.instSMul SMulZeroClass.toSMul Complex AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass ESeminormedAddMonoid.toAddMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ESeminormedAddCommMonoid.toESeminormedAddMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Complex.instSemiring Module.toDistribMulAction ESeminormedAddCommMonoid.toAddCommMonoid NormedSpace.toModule Complex.instNormedField DFunLike.coe AddChar Real Real.instAddMonoid DivInvMonoid.toMonoid Group.toDivInvMonoid CommGroup.toGroup Circle.instCommGroup AddChar.instFunLike Real.fourierChar Real.instNeg Inner.inner InnerProductSpace.toInner Real.instRCLike AddCommMagma.toAdd AddCommSemigroup.toAddCommMagma AddCommMonoid.toAddCommSemigroup NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedAddCommGroup.toAddCommGroup	—	Nat.instAtLeastTwoHAddOfNat inner_smul_left inner_self_eq_norm_sq_to_K RCLike.ofReal_real_eq_id RCLike.conj_to_real div_div div_mul_cancel₀ sq_eq_zero_iff isReduced_of_noZeroDivisors NormMulClass.toNoZeroDivisors NormedDivisionRing.toNormMulClass norm_eq_zero inner_add_left neg_add mul_add Distrib.leftDistribClass Complex.ofReal_add add_mul Distrib.rightDistribClass Complex.exp_add Mathlib.Tactic.Module.NF.eq_of_eval_eq_eval Mathlib.Tactic.Module.NF.smul_eq_eval Mathlib.Tactic.Module.NF.atom_eq_eval Mathlib.Tactic.Module.NF.eval_algebraMap AddCommMonoid.nat_isScalarTower Mathlib.Tactic.Module.NF.neg_eq_eval Mathlib.Tactic.Module.NF.eq_cons_cons Complex.ofReal_mul Complex.ofReal_neg eq_natCast RingHom.instRingHomClass Nat.cast_one Complex.ofReal_div Complex.exp_neg Complex.exp_pi_mul_I Mathlib.Tactic.LinearCombination.eq_of_eq AddRightCancelSemigroup.toIsRightCancelAdd Mathlib.Tactic.LinearCombination.mul_const_eq Mathlib.Tactic.LinearCombination.eq_rearrange Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.atom_pf' Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Meta.NormNum.instAtLeastTwo Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.mul_one Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.RingNF.nat_rawCast_1 pow_one Mathlib.Tactic.RingNF.int_rawCast_neg Mathlib.Tactic.RingNF.mul_neg Mathlib.Tactic.RingNF.mul_assoc_rev add_zero Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.inv_congr Mathlib.Tactic.Ring.inv_single Mathlib.Meta.NormNum.IsRat.to_isInt Mathlib.Meta.NormNum.isRat_inv_neg Complex.instCharZero Mathlib.Meta.NormNum.IsInt.to_isRat Mathlib.Tactic.Ring.add_pf_add_overlap_zero Mathlib.Tactic.Ring.add_overlap_pf_zero Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Meta.NormNum.isInt_add Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.div_congr Mathlib.Tactic.Ring.div_pf Mathlib.Meta.NormNum.IsNNRat.to_raw_eq Mathlib.Meta.NormNum.isNNRat_inv_pos Mathlib.Meta.NormNum.IsNat.to_isNNRat Mathlib.Meta.NormNum.IsRat.to_raw_eq Mathlib.Meta.NormNum.isRat_mul Mathlib.Meta.NormNum.IsNNRat.to_isRat Mathlib.Meta.NormNum.IsNNRat.of_raw Mathlib.Meta.NormNum.IsNNRat.den_nz Mathlib.Meta.NormNum.IsRat.of_raw Mathlib.Meta.NormNum.IsRat.den_nz mul_one Mathlib.Tactic.Ring.sub_pf MeasureTheory.integral_add_right_eq_self ContinuousAdd.measurableAdd IsTopologicalAddGroup.toContinuousAdd SeminormedAddCommGroup.toIsTopologicalAddGroup MeasureTheory.IsAddLeftInvariant.isAddRightInvariant MeasureTheory.Measure.IsAddHaarMeasure.toIsAddLeftInvariant instIsAddHaarMeasureVolume MeasureTheory.integral_neg
tendsto_integral_exp_inner_smul_cocompact 📖	mathematical	—	Filter.Tendsto MeasureTheory.integral NormedSpace.complexToReal NormedAddCommGroup.toSeminormedAddCommGroup MeasureTheory.MeasureSpace.toMeasurableSpace measureSpaceOfInnerProductSpace MeasureTheory.MeasureSpace.volume Circle Circle.instSMul SMulZeroClass.toSMul Complex AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass ESeminormedAddMonoid.toAddMonoid UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace ESeminormedAddCommMonoid.toESeminormedAddMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Complex.instSemiring Module.toDistribMulAction ESeminormedAddCommMonoid.toAddCommMonoid NormedSpace.toModule Complex.instNormedField DFunLike.coe AddChar Real Real.instAddMonoid DivInvMonoid.toMonoid Group.toDivInvMonoid CommGroup.toGroup Circle.instCommGroup AddChar.instFunLike Real.fourierChar Real.instNeg Inner.inner InnerProductSpace.toInner Real.instRCLike Filter.cocompact nhds NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedAddCommGroup.toAddCommGroup	—	Metric.tendsto_nhds Nat.instAtLeastTwoHAddOfNat MeasureTheory.Integrable.exists_hasCompactSupport_integral_sub_le PerfectlyNormalSpace.toNormalSpace T6Space.toPerfectlyNormalSpace instT6SpaceOfMetrizableSpace EMetricSpace.metrizableSpace instR1Space TopologicalSpace.PseudoMetrizableSpace.regularSpace PseudoEMetricSpace.pseudoMetrizableSpace instWeaklyLocallyCompactSpaceOfLocallyCompactSpace locallyCompact_of_proper FiniteDimensional.proper_real MeasureTheory.Measure.Regular.of_sigmaCompactSpace_of_isLocallyFiniteMeasure SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace SeminormedAddCommGroup.toIsTopologicalAddGroup TopologicalSpace.SecondCountableTopology.to_separableSpace secondCountable_of_proper MeasureTheory.isLocallyFiniteMeasure_of_isFiniteMeasureOnCompacts MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts instIsAddHaarMeasureVolume div_pos PosMulReflectLE.toPosMulReflectLT PosMulStrictMono.toPosMulReflectLE IsStrictOrderedRing.toPosMulStrictMono Real.instIsStrictOrderedRing two_pos Real.instZeroLEOneClass NeZero.charZero_one RCLike.charZero_rclike IsOrderedAddMonoid.toAddLeftMono Real.instIsOrderedAddMonoid Filter.Eventually.mp tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_support Filter.Eventually.of_forall dist_eq_norm le_trans MeasureTheory.integral_sub Real.fourierIntegral_convergent_iff Continuous.integrable_of_hasCompactSupport BorelSpace.opensMeasurable VectorFourier.norm_fourierIntegral_le_integral_norm add_lt_add_of_le_of_lt IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono AddLeftCancelSemigroup.toIsLeftCancelAdd covariant_swap_add_of_covariant_add LE.le.trans_lt LE.le.trans le_of_eq sub_zero sub_add_cancel norm_add_le add_halves CharZero.NeZero.two MeasureTheory.integral_undef tendsto_const_nhds
tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_support 📖	mathematical	Continuous UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup HasCompactSupport NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedAddCommGroup.toAddCommGroup	Filter.Tendsto MeasureTheory.integral NormedSpace.complexToReal MeasureTheory.MeasureSpace.toMeasurableSpace measureSpaceOfInnerProductSpace MeasureTheory.MeasureSpace.volume Circle Circle.instSMul SMulZeroClass.toSMul Complex AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass ESeminormedAddMonoid.toAddMonoid ESeminormedAddCommMonoid.toESeminormedAddMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Complex.instSemiring Module.toDistribMulAction ESeminormedAddCommMonoid.toAddCommMonoid NormedSpace.toModule Complex.instNormedField DFunLike.coe AddChar Real Real.instAddMonoid DivInvMonoid.toMonoid Group.toDivInvMonoid CommGroup.toGroup Circle.instCommGroup AddChar.instFunLike Real.fourierChar Real.instNeg Inner.inner InnerProductSpace.toInner Real.instRCLike Filter.cocompact nhds	—	NormedAddCommGroup.tendsto_nhds_zero HasCompactSupport.exists_pos_le_norm dist_eq_norm sub_zero IsClosed.measurableSet BorelSpace.opensMeasurable Metric.isClosed_closedBall ProperSpace.isCompact_closedBall FiniteDimensional.proper_real IsCompact.measure_lt_top MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts instIsAddHaarMeasureVolume add_pos_of_nonneg_of_pos IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono AddLeftCancelSemigroup.toIsLeftCancelAdd NNReal.addLeftMono NNReal.coe_nonneg one_pos LinearOrderedCommMonoidWithZero.toZeroLeOneClass NeZero.charZero_one IsStrictOrderedRing.toCharZero NNReal.instIsStrictOrderedRing ENNReal.coe_add ENNReal.coe_one ENNReal.coe_toNNReal LT.lt.ne le_self_add ENNReal.instCanonicallyOrderedAdd Metric.uniformContinuous_iff HasCompactSupport.uniformContinuous_of_continuous div_pos PosMulReflectLE.toPosMulReflectLT PosMulStrictMono.toPosMulReflectLE IsStrictOrderedRing.toPosMulStrictMono Real.instIsStrictOrderedRing Nat.instAtLeastTwoHAddOfNat Mathlib.Tactic.Contrapose.contrapose₃ norm_zero add_pos IsOrderedAddMonoid.toAddLeftMono Real.instIsOrderedAddMonoid one_half_pos one_div_pos mul_pos two_pos Real.instZeroLEOneClass RCLike.charZero_rclike norm_smul NormedSpace.toNormSMulClass norm_div Real.norm_of_nonneg mul_nonneg IsOrderedRing.toPosMulMono Real.instIsOrderedRing LT.lt.le sq_nonneg AddGroup.existsAddOfLE NormOneClass.norm_one NormedDivisionRing.to_normOneClass sq div_div div_mul_cancel₀ Iff.not norm_eq_zero one_div norm_inv Complex.norm_ofNat fourierIntegral_eq_half_sub_half_period_translate Continuous.integrable_of_hasCompactSupport inv_mul_eq_div div_lt_iff₀' lt_of_le_of_lt MeasureTheory.norm_integral_le_integral_norm Circle.norm_smul MeasureTheory.setIntegral_eq_integral_of_forall_compl_eq_zero LE.le.trans le_add_of_nonneg_right zero_le_one sub_neg_eq_add le_trans le_sub_iff_add_le covariant_swap_add_of_covariant_add norm_neg add_le_add_iff_left IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT contravariant_lt_of_covariant_le div_le_one norm_pos_iff one_div_nonneg zero_lt_two' norm_sub_norm_le norm_norm sub_add_cancel_left div_lt_iff₀ MulPosReflectLE.toMulPosReflectLT MulPosStrictMono.toMulPosReflectLE IsStrictOrderedRing.toMulPosStrictMono LT.lt.trans_le lt_add_of_pos_left IsRightCancelAdd.addRightStrictMono_of_addRightMono AddRightCancelSemigroup.toIsRightCancelAdd MeasureTheory.norm_setIntegral_le_of_norm_le_const LE.le.trans_lt ENNReal.coe_lt_top MeasureTheory.setIntegral_nonneg norm_nonneg div_mul_eq_mul_div NNReal.coe_pos mul_comm mul_assoc mul_lt_mul_iff_right₀ ENNReal.toReal_mono ENNReal.coe_ne_top ENNReal.coe_toReal two_mul comap_dist_left_atTop_eq_cocompact instIsDirectedOrder Real.instArchimedean dist_eq_norm'
tendsto_integral_exp_smul_cocompact 📖	mathematical	—	Filter.Tendsto StrongDual Real Real.semiring UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.pseudoMetricSpace AddCommGroup.toAddCommMonoid MeasureTheory.integral NormedSpace.complexToReal NormedAddCommGroup.toSeminormedAddCommGroup Circle Circle.instSMul SMulZeroClass.toSMul Complex AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass ESeminormedAddMonoid.toAddMonoid SeminormedAddCommGroup.toPseudoMetricSpace ESeminormedAddCommMonoid.toESeminormedAddMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Complex.instSemiring Module.toDistribMulAction ESeminormedAddCommMonoid.toAddCommMonoid NormedSpace.toModule Complex.instNormedField DFunLike.coe AddChar Real.instAddMonoid DivInvMonoid.toMonoid Group.toDivInvMonoid CommGroup.toGroup Circle.instCommGroup AddChar.instFunLike Real.fourierChar Real.instNeg ContinuousLinearMap.funLike RingHom.id Semiring.toNonAssocSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule Filter.cocompact ContinuousLinearMap.topologicalSpace Real.normedField Real.instAddCommGroup instIsTopologicalAddGroupReal nhds NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedAddCommGroup.toAddCommGroup	—	RingHomInvPair.ids fact_one_le_two_ennreal instIsTopologicalAddGroupReal IsTopologicalSemiring.toContinuousAdd IsTopologicalRing.toIsTopologicalSemiring instIsTopologicalRingReal Algebra.to_smulCommClass UniformContinuousConstSMul.to_continuousConstSMul Ring.uniformContinuousConstSMul instIsUniformAddGroupReal IsTopologicalSemiring.toContinuousMul RingHomCompTriple.ids RingHomIsometric.ids ContinuousLinearEquiv.isAddHaarMeasure_map SeminormedAddCommGroup.toIsTopologicalAddGroup ContinuousLinearEquiv.symm_apply_apply MeasureTheory.integral_map_equiv ContinuousLinearMap.id_comp Filter.Tendsto.comp tendsto_integral_exp_smul_cocompact_of_inner_product WithLp.instModuleFinite FiniteDimensional.finiteDimensional_pi' Finite.of_fintype FiniteDimensional.rclike_to_real CocompactMap.cocompact_tendsto'
tendsto_integral_exp_smul_cocompact_of_inner_product 📖	mathematical	—	Filter.Tendsto StrongDual Real Real.semiring UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.pseudoMetricSpace SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup ESeminormedAddCommMonoid.toAddCommMonoid ENormedAddCommMonoid.toESeminormedAddCommMonoid NormedAddCommGroup.toENormedAddCommMonoid NormedSpace.toModule Real.normedField InnerProductSpace.toNormedSpace Real.instRCLike MeasureTheory.integral NormedSpace.complexToReal Circle Circle.instSMul SMulZeroClass.toSMul Complex AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass ESeminormedAddMonoid.toAddMonoid ESeminormedAddCommMonoid.toESeminormedAddMonoid DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Complex.instSemiring Module.toDistribMulAction Complex.instNormedField DFunLike.coe AddChar Real.instAddMonoid DivInvMonoid.toMonoid Group.toDivInvMonoid CommGroup.toGroup Circle.instCommGroup AddChar.instFunLike Real.fourierChar Real.instNeg ContinuousLinearMap.funLike RingHom.id Semiring.toNonAssocSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule Filter.cocompact ContinuousLinearMap.topologicalSpace SeminormedAddCommGroup.toAddCommGroup Real.instAddCommGroup instIsTopologicalAddGroupReal nhds NegZeroClass.toZero SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid NormedAddCommGroup.toAddCommGroup	—	instIsTopologicalAddGroupReal IsScalarTower.right SeminormedAddCommGroup.toIsTopologicalAddGroup instIsAddHaarMeasureVolume MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts MeasureTheory.Measure.IsAddHaarMeasure.toIsAddLeftInvariant MeasureTheory.Measure.isAddLeftInvariant_eq_smul locallyCompact_of_proper FiniteDimensional.proper_real secondCountable_of_proper MeasureTheory.integral_smul_nnreal_measure smul_zero Filter.Tendsto.const_smul ContinuousSMul.continuousConstSMul NNReal.instContinuousSMulOfReal IsBoundedSMul.continuousSMul NormedSpace.toIsBoundedSMul RingHomInvPair.instStarRingEnd RingHomIsometric.ids Algebra.to_smulCommClass UniformContinuousConstSMul.to_continuousConstSMul Ring.uniformContinuousConstSMul SeminormedAddCommGroup.to_isUniformAddGroup IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring IsTopologicalDivisionRing.toIsTopologicalRing NormedDivisionRing.to_isTopologicalDivisionRing complete_of_proper inner_conj_symm RCLike.conj_to_real InnerProductSpace.toDual_symm_apply Filter.Tendsto.comp tendsto_integral_exp_inner_smul_cocompact CocompactMap.cocompact_tendsto'

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