NonIntegrable

📁 Source: Mathlib/Analysis/SpecialFunctions/NonIntegrable.lean

Statistics

Metric	Count
Definitions	0
Theorems intervalIntegrable_inv_iff, intervalIntegrable_sub_inv_iff, not_IntegrableOn_Ici_inv, not_IntegrableOn_Ioi_inv, not_integrableOn_Ici_inv, not_integrableOn_Ioi_inv, not_integrableOn_of_tendsto_norm_atTop_of_deriv_isBigO_filter, not_integrableOn_of_tendsto_norm_atTop_of_deriv_isBigO_filter_aux, not_intervalIntegrable_of_sub_inv_isBigO_punctured, not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter, not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_punctured, not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_within_diff_singleton	12
Total	12

(root)

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
intervalIntegrable_inv_iff 📖	mathematical	—	IntervalIntegrable Real UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.pseudoMetricSpace NormedAddGroup.toENormedAddMonoid NormedAddCommGroup.toNormedAddGroup Real.normedAddCommGroup Real.instInv MeasureTheory.MeasureSpace.volume Real.measureSpace Set Set.instMembership Set.uIcc Real.lattice Real.instZero	—	sub_zero
intervalIntegrable_sub_inv_iff 📖	mathematical	—	IntervalIntegrable Real UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.pseudoMetricSpace NormedAddGroup.toENormedAddMonoid NormedAddCommGroup.toNormedAddGroup Real.normedAddCommGroup Real.instInv Real.instSub MeasureTheory.MeasureSpace.volume Real.measureSpace Set Set.instMembership Set.uIcc Real.lattice	—	not_intervalIntegrable_of_sub_inv_isBigO_punctured Asymptotics.isBigO_refl IntervalIntegrable.refl ContinuousOn.intervalIntegrable Real.locallyFinite_volume ContinuousOn.inv₀ IsTopologicalDivisionRing.toContinuousInv₀ instIsTopologicalDivisionRingReal Continuous.continuousOn continuous_sub_right IsTopologicalAddGroup.to_continuousSub instIsTopologicalAddGroupReal sub_ne_zero
not_IntegrableOn_Ici_inv 📖	mathematical	—	MeasureTheory.IntegrableOn Real MeasureTheory.MeasureSpace.toMeasurableSpace Real.measureSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.pseudoMetricSpace SeminormedAddGroup.toContinuousENorm SeminormedAddCommGroup.toSeminormedAddGroup NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing Real.normedCommRing Real.instInv Set.Ici Real.instPreorder MeasureTheory.MeasureSpace.volume	—	not_integrableOn_Ici_inv
not_IntegrableOn_Ioi_inv 📖	mathematical	—	MeasureTheory.IntegrableOn Real MeasureTheory.MeasureSpace.toMeasurableSpace Real.measureSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.pseudoMetricSpace SeminormedAddGroup.toContinuousENorm SeminormedAddCommGroup.toSeminormedAddGroup NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing Real.normedCommRing Real.instInv Set.Ioi Real.instPreorder MeasureTheory.MeasureSpace.volume	—	not_integrableOn_Ioi_inv
not_integrableOn_Ici_inv 📖	mathematical	—	MeasureTheory.IntegrableOn Real MeasureTheory.MeasureSpace.toMeasurableSpace Real.measureSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.pseudoMetricSpace SeminormedAddGroup.toContinuousENorm SeminormedAddCommGroup.toSeminormedAddGroup NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing Real.normedCommRing Real.instInv Set.Ici Real.instPreorder MeasureTheory.MeasureSpace.volume	—	IsModuleTopology.toContinuousSMul IsTopologicalSemiring.toIsModuleTopology IsTopologicalRing.toIsTopologicalSemiring instIsTopologicalRingReal Filter.mp_mem Filter.Ioi_mem_atTop instNoTopOrderOfNoMaxOrder instNoMaxOrderOfNontrivial Real.instIsOrderedRing Real.instNontrivial Filter.univ_mem' Real.hasDerivAt_log ne_of_gt Filter.Tendsto.comp tendsto_norm_atTop_atTop Real.tendsto_log_atTop not_integrableOn_of_tendsto_norm_atTop_of_deriv_isBigO_filter Filter.atTop_neBot instIsDirectedOrder Real.instArchimedean Filter.tendsto_Icc_atTop_atTop Filter.Ici_mem_atTop Filter.Eventually.mono HasDerivAt.differentiableAt Filter.EventuallyEq.isBigO HasDerivAt.deriv
not_integrableOn_Ioi_inv 📖	mathematical	—	MeasureTheory.IntegrableOn Real MeasureTheory.MeasureSpace.toMeasurableSpace Real.measureSpace UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.pseudoMetricSpace SeminormedAddGroup.toContinuousENorm SeminormedAddCommGroup.toSeminormedAddGroup NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing Real.normedCommRing Real.instInv Set.Ioi Real.instPreorder MeasureTheory.MeasureSpace.volume	—	MeasureTheory.restrict_Ioi_eq_restrict_Ici Real.noAtoms_volume not_integrableOn_Ici_inv
not_integrableOn_of_tendsto_norm_atTop_of_deriv_isBigO_filter 📖	mathematical	Set Real Filter Filter.instMembership Filter.Eventually DifferentiableAt DenselyNormedField.toNontriviallyNormedField Real.denselyNormedField Real.instAddCommGroup NormedSpace.toModule Real.normedField NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing Real.normedCommRing InnerProductSpace.toNormedSpace Real.instRCLike RCLike.toInnerProductSpaceReal UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.pseudoMetricSpace NormedAddCommGroup.toAddCommGroup NormedAddCommGroup.toSeminormedAddCommGroup SeminormedAddCommGroup.toPseudoMetricSpace Filter.Tendsto Norm.norm NormedAddCommGroup.toNorm Filter.atTop Real.instPreorder Asymptotics.IsBigO deriv	MeasureTheory.IntegrableOn MeasureTheory.MeasureSpace.toMeasurableSpace Real.measureSpace SeminormedAddGroup.toContinuousENorm SeminormedAddCommGroup.toSeminormedAddGroup MeasureTheory.MeasureSpace.volume	—	SeminormedAddCommGroup.to_isUniformAddGroup IsBoundedSMul.toUniformContinuousConstSMul NormedSpace.toIsBoundedSMul Filter.mp_mem Filter.univ_mem' DifferentiableAt.comp ContinuousLinearMap.differentiableAt Filter.Tendsto.congr LinearIsometry.norm_map Asymptotics.IsBigO.trans Asymptotics.isBigO_norm_norm fderiv_comp_deriv ContinuousLinearMap.fderiv IsTopologicalAddGroup.toContinuousAdd SeminormedAddCommGroup.toIsTopologicalAddGroup IsBoundedSMul.continuousSMul UniformSpace.Completion.instIsBoundedSMul TopologicalSpace.t2Space_of_metrizableSpace EMetricSpace.metrizableSpace Filter.EventuallyEq.isBigO not_integrableOn_of_tendsto_norm_atTop_of_deriv_isBigO_filter_aux UniformSpace.Completion.completeSpace
not_integrableOn_of_tendsto_norm_atTop_of_deriv_isBigO_filter_aux 📖	mathematical	Set Real Filter Filter.instMembership Filter.Eventually DifferentiableAt DenselyNormedField.toNontriviallyNormedField Real.denselyNormedField Real.instAddCommGroup NormedSpace.toModule Real.normedField NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing Real.normedCommRing InnerProductSpace.toNormedSpace Real.instRCLike RCLike.toInnerProductSpaceReal UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.pseudoMetricSpace NormedAddCommGroup.toAddCommGroup NormedAddCommGroup.toSeminormedAddCommGroup SeminormedAddCommGroup.toPseudoMetricSpace Filter.Tendsto Norm.norm NormedAddCommGroup.toNorm Filter.atTop Real.instPreorder Asymptotics.IsBigO deriv	MeasureTheory.IntegrableOn MeasureTheory.MeasureSpace.toMeasurableSpace Real.measureSpace SeminormedAddGroup.toContinuousENorm SeminormedAddCommGroup.toSeminormedAddGroup MeasureTheory.MeasureSpace.volume	—	Asymptotics.IsBigO.exists_nonneg Filter.Tendsto.eventually Filter.Tendsto.uIcc Filter.tendsto_fst Filter.tendsto_snd Filter.Eventually.smallSets Filter.Eventually.and Asymptotics.IsBigOWith.bound Filter.mem_prod_self_iff MeasureTheory.Integrable.smul Real.isBoundedSMul MeasureTheory.Integrable.norm Filter.nonempty_of_mem Filter.eventually_gt_atTop instNoTopOrderOfNoMaxOrder instNoMaxOrderOfNontrivial Real.instIsOrderedRing Real.instNontrivial Filter.Eventually.exists LT.lt.le MeasureTheory.Measure.instOuterMeasureClass Filter.Eventually.mono MeasureTheory.ae_restrict_mem measurableSet_uIoc BorelSpace.opensMeasurable Real.borelSpace instClosedIicTopology HasSolidNorm.orderClosedTopology instHasSolidNormReal Real.instIsOrderedAddMonoid Set.Subset.trans Set.Ioc_subset_Icc_self intervalIntegrable_iff PseudoEMetricSpace.pseudoMetrizableSpace MeasureTheory.IntegrableOn.mono le_rfl MeasureTheory.Integrable.mono' aestronglyMeasurable_deriv secondCountableTopologyEither_of_left instSecondCountableTopologyReal LT.lt.not_ge sub_le_iff_le_add' IsOrderedAddMonoid.toAddLeftMono norm_sub_norm_le intervalIntegral.integral_deriv_eq_sub intervalIntegral.norm_integral_eq_norm_integral_uIoc MeasureTheory.norm_integral_le_integral_norm MeasureTheory.setIntegral_mono_on IsStrictOrderedModule.toIsOrderedModule IsStrictOrderedRing.toIsStrictOrderedModule Real.instIsStrictOrderedRing instClosedIciTopology IntervalIntegrable.def' IntervalIntegrable.norm MeasureTheory.IntegrableOn.mono_set MeasureTheory.setIntegral_mono_set MeasureTheory.ae_of_all mul_nonneg IsOrderedRing.toPosMulMono norm_nonneg HasSubset.Subset.eventuallyLE
not_intervalIntegrable_of_sub_inv_isBigO_punctured 📖	mathematical	Asymptotics.IsBigO Real Real.norm NormedAddCommGroup.toNorm nhdsWithin UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.pseudoMetricSpace Compl.compl Set Set.instCompl Set.instSingletonSet Real.instInv Real.instSub Set.instMembership Set.uIcc Real.lattice	IntervalIntegrable SeminormedAddCommGroup.toPseudoMetricSpace NormedAddCommGroup.toSeminormedAddCommGroup NormedAddGroup.toENormedAddMonoid NormedAddCommGroup.toNormedAddGroup MeasureTheory.MeasureSpace.volume Real.measureSpace	—	IsModuleTopology.toContinuousSMul IsTopologicalSemiring.toIsModuleTopology IsTopologicalRing.toIsTopologicalSemiring instIsTopologicalRingReal Filter.mp_mem self_mem_nhdsWithin Filter.univ_mem' ContinuousMul.to_continuousSMul IsTopologicalSemiring.toContinuousMul HasDerivAt.congr_simp one_div HasDerivAt.log HasDerivAt.sub_const hasDerivAt_id sub_ne_zero Filter.Tendsto.comp Filter.tendsto_abs_atBot_atTop Real.instIsOrderedAddMonoid Real.tendsto_log_nhdsNE_zero sub_self HasDerivAt.tendsto_nhdsNE one_ne_zero NeZero.charZero_one RCLike.charZero_rclike not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_punctured Filter.Eventually.mono HasDerivAt.differentiableAt Asymptotics.IsBigO.congr' HasDerivAt.deriv Filter.EventuallyEq.rfl
not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter 📖	mathematical	Set Real Filter Filter.instMembership Set.uIcc Real.lattice Filter.Eventually DifferentiableAt DenselyNormedField.toNontriviallyNormedField Real.denselyNormedField Real.instAddCommGroup NormedSpace.toModule Real.normedField NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing Real.normedCommRing InnerProductSpace.toNormedSpace Real.instRCLike RCLike.toInnerProductSpaceReal UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.pseudoMetricSpace NormedAddCommGroup.toAddCommGroup NormedAddCommGroup.toSeminormedAddCommGroup SeminormedAddCommGroup.toPseudoMetricSpace Filter.Tendsto Norm.norm NormedAddCommGroup.toNorm Filter.atTop Real.instPreorder Asymptotics.IsBigO deriv	IntervalIntegrable NormedAddGroup.toENormedAddMonoid NormedAddCommGroup.toNormedAddGroup MeasureTheory.MeasureSpace.volume Real.measureSpace	—	intervalIntegrable_iff' PseudoEMetricSpace.pseudoMetrizableSpace Real.noAtoms_volume enorm_ne_top not_integrableOn_of_tendsto_norm_atTop_of_deriv_isBigO_filter
not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_punctured 📖	mathematical	Filter.Eventually Real DifferentiableAt DenselyNormedField.toNontriviallyNormedField Real.denselyNormedField Real.instAddCommGroup NormedSpace.toModule Real.normedField NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing Real.normedCommRing InnerProductSpace.toNormedSpace Real.instRCLike RCLike.toInnerProductSpaceReal UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.pseudoMetricSpace NormedAddCommGroup.toAddCommGroup NormedAddCommGroup.toSeminormedAddCommGroup SeminormedAddCommGroup.toPseudoMetricSpace nhdsWithin Compl.compl Set Set.instCompl Set.instSingletonSet Filter.Tendsto Norm.norm NormedAddCommGroup.toNorm Filter.atTop Real.instPreorder Asymptotics.IsBigO deriv Set.instMembership Set.uIcc Real.lattice	IntervalIntegrable NormedAddGroup.toENormedAddMonoid NormedAddCommGroup.toNormedAddGroup MeasureTheory.MeasureSpace.volume Real.measureSpace	—	nhdsWithin_mono Set.inter_subset_right not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_within_diff_singleton Filter.Eventually.filter_mono Filter.Tendsto.mono_left Asymptotics.IsBigO.mono
not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_within_diff_singleton 📖	mathematical	Real Set Set.instMembership Set.uIcc Real.lattice Filter.Eventually DifferentiableAt DenselyNormedField.toNontriviallyNormedField Real.denselyNormedField Real.instAddCommGroup NormedSpace.toModule Real.normedField NonUnitalSeminormedRing.toSeminormedAddCommGroup NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing SeminormedCommRing.toNonUnitalSeminormedCommRing NormedCommRing.toSeminormedCommRing Real.normedCommRing InnerProductSpace.toNormedSpace Real.instRCLike RCLike.toInnerProductSpaceReal UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.pseudoMetricSpace NormedAddCommGroup.toAddCommGroup NormedAddCommGroup.toSeminormedAddCommGroup SeminormedAddCommGroup.toPseudoMetricSpace nhdsWithin Set.instSDiff Set.instSingletonSet Filter.Tendsto Norm.norm NormedAddCommGroup.toNorm Filter.atTop Real.instPreorder Asymptotics.IsBigO deriv	IntervalIntegrable NormedAddGroup.toENormedAddMonoid NormedAddCommGroup.toNormedAddGroup MeasureTheory.MeasureSpace.volume Real.measureSpace	—	LT.lt.gt_or_lt min_lt_max tendstoIxxNhdsWithin tendstoIccClassNhds instOrderTopologyReal Filter.OrdConnected.tendsto_Icc Set.ordConnected_Iio nhdsLT_neBot LinearOrderedSemiField.toDenselyOrdered PosMulReflectLE.toPosMulReflectLT PosMulStrictMono.toPosMulReflectLE IsStrictOrderedRing.toPosMulStrictMono Real.instIsStrictOrderedRing instNoMinOrderOfNontrivial Real.instIsOrderedRing Real.instNontrivial inf_le_left Set.Iic_diff_right diff_mem_nhdsWithin_diff Icc_mem_nhdsLE_of_mem instClosedIicTopology HasSolidNorm.orderClosedTopology instHasSolidNormReal Real.instIsOrderedAddMonoid Set.ordConnected_Ioi nhdsGT_neBot instNoMaxOrderOfNontrivial Set.Ici_diff_left Icc_mem_nhdsGE_of_mem instClosedIciTopology le_inf Filter.le_principal_iff not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter Filter.mem_of_superset Set.diff_subset Filter.Eventually.filter_mono Filter.Tendsto.mono_left Asymptotics.IsBigO.mono

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