Documentation Verification Report

MeasurePreserving

πŸ“ Source: Mathlib/Dynamics/Ergodic/MeasurePreserving.lean

Statistics

MetricCount
DefinitionsMeasurePreserving
1
TheoremsmeasurePreserving, measurePreserving_symm, add_measure, aeconst_comp, aeconst_preimage, aemeasurable, aemeasurable_comp_iff, comp, comp_left_iff, comp_right_iff, exists_mem_iterate_mem, exists_mem_iterate_mem_of_measure_univ_lt_mul_measure, id, iterate, map_eq, map_of_comp, measurable, measureReal_preimage, measure_preimage, measure_preimage_emb, measure_preimage_equiv, measure_preimage_le, measure_symmDiff_preimage_iterate_le, of_isEmpty, of_semiconj, preimage_null, quasiMeasurePreserving, restrict_image_emb, restrict_preimage, restrict_preimage_emb, sfinite, sigmaFinite, smul_measure, trans, measurePreserving_subtype_coe
35
Total36

Measurable

Theorems

NameKindAssumesProvesValidatesDepends On
measurePreserving πŸ“–mathematicalMeasurableMeasureTheory.MeasurePreserving
MeasureTheory.Measure.map
β€”β€”

MeasureTheory

Definitions

NameCategoryTheorems
MeasurePreserving πŸ“–CompData
152 mathmath: volume_preserving_arrowCongr', Measure.measurePreserving_sub_left, smulInvariantMeasure_iterateMulAct, volume_preserving_pi, measurePreserving_prod_mul_swap, Measure.measurePreserving_neg, measurePreserving_prod_neg_add, measurePreserving_funUnique, unitInterval.measurePreserving_coe, ProbabilityTheory.measurePreserving_restrictβ‚‚_multivariateGaussian, MeasurePreserving.restrict_preimage, volume_measurePreserving_piCongrLeft, measurePreserving_div_right, measurePreserving_prod_mul_swap_right, measurePreserving_pi, measurePreserving_prod_div_swap, measurePreserving_prod_inv_mul_swap, OrthonormalBasis.measurePreserving_repr, measurePreserving_mul_left, volume_preserving_piFinsetUnion, MeasurePreserving.prod, measurePreserving_finTwoArrow_vec, MeasurePreserving.symm, measurePreserving_mul_prod_inv_right, LinearIsometryEquiv.measurePreserving, hausdorffMeasure_measurePreserving_piFinTwo, volume_preserving_prodAssoc, unitInterval.measurePreserving_symm, MeasurePreserving.comp_right_iff, measurePreserving_sub_right, measurePreserving_vadd, IsAddFundamentalDomain.measurePreserving_add_quotient_mk, PiLp.volume_preserving_toLp, Measure.measurePreserving_zsmul, Measurable.measurePreserving, Ergodic.iff_mem_extremePoints_measure_univ_eq, MeasurePreserving.add_measure, measurePreserving_prod_add_right, volume_preserving_piFinSuccAbove, MeasurePreserving.restrict_image_emb, MeasurePreserving.smul_measure, MeasurePreserving.withDensity_rnDeriv, measurePreserving_eval, measurePreserving_piCongrLeft, measurePreserving_add_prod_neg_right, measurePreserving_arrowCongr', measurePreserving_arrowProdEquivProdArrow, Ergodic.toMeasurePreserving, UnitAddTorus.measurePreserving_equivPiIoc, volume_preserving_pi_empty, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, measurePreserving_prod_sub_swap, NumberField.mixedEmbedding.volume_preserving_negAt, measurePreserving_piFinTwo, MeasurePreserving.iterate, Measure.measurePreserving_div_left, measurePreserving_prod_div, WithLp.volume_preserving_toLp, PiLp.volume_preserving_ofLp, measurePreserving_prodAssoc, NumberField.mixedEmbedding.volume_preserving_mixedSpaceToRealMixedSpace_symm, ProbabilityTheory.HasLaw.measurePreserving, Measure.MeasurePreserving.zsmul, measurePreserving_piFinSuccAbove, measurePreserving_eval_infinitePi, IsometryEquiv.measurePreserving_hausdorffMeasure, Complex.volume_preserving_equiv_real_prod, Measure.measurePreserving_homeomorphUnitSphereProd, AddCircle.measurePreserving_equivIoc, measurePreserving_piUnique, EuclideanGeometry.measurePreserving_vaddConst, MeasurePreserving.add_left, hausdorffMeasure_measurePreserving_funUnique, OrthonormalBasis.measurePreserving_repr_symm, UnitAddCircle.measurePreserving_mk, MeasurePreserving.of_semiconj, MeasurePreserving.singularPart, Measure.measurePreserving_add_right_neg, volume_preserving_piFinTwo, measurePreserving_subtype_coe, measurePreserving_prod_sub, vaddInvariantMeasure_iterateAddAct, EuclideanSpace.volume_preserving_symm_measurableEquiv_toLp, measurePreserving_smul, measurePreserving_prod_add, measurePreserving_mul_prod, WithLp.volume_preserving_symm_measurableEquiv_toLp_prod, Complex.volume_preserving_equiv_pi, NumberField.mixedEmbedding.volume_preserving_homeoRealMixedSpacePolarSpace, MeasurePreserving.map_of_comp, measurePreserving_prod_add_swap_right, Ergodic.iff_mem_extremePoints, measurePreserving_add_prod, ProbabilityTheory.measurePreserving_eval_multivariateGaussian, measurePreserving_piFinsetUnion, MeasurePreserving.mul_right, volume_measurePreserving_arrowProdEquivProdArrow, WithLp.volume_preserving_ofLp, MeasurePreserving.comp_left_iff, AddCircle.measurePreserving_mk, Ergodic.mem_extremePoints_measure_univ_eq, volume_preserving_piUnique, Measure.measurePreserving_inv, MeasurePreserving.add_right, measurePreserving_add_left, measurePreserving_add_right, MeasurePreserving.congr, measurePreserving_mul_right, measurePreserving_quotientAddGroup_mk_of_AddQuotientMeasureEqMeasurePreimage, MeasurePreserving.skew_product, Measure.MeasurePreserving.zpow, measurePreserving_prod_add_swap, measurePreserving_prod_mul, MeasurePreserving.mul_left, MeasurePreserving.comp, Lp.compMeasurePreserving_continuous, measurePreserving_prod_inv_mul, measurePreserving_sumPiEquivProdPi_symm, MeasurePreserving.id, measurePreserving_snd, measurePreserving_mul_prod_inv, AddMonoidHom.measurePreserving, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, measurePreserving_piEquivPiSubtypeProd, Measure.measurePreserving_swap, volume_preserving_finTwoArrow, Measure.measurePreserving_mul_right_inv, measurePreserving_quotientGroup_mk_of_QuotientMeasureEqMeasurePreimage, measurePreserving_pi_empty, MeasurePreserving.of_isEmpty, MonoidHom.measurePreserving, measurePreserving_finTwoArrow, Measure.measurePreserving_zpow, IsometryEquiv.measurePreserving_euclideanHausdorffMeasure, OrthonormalBasis.measurePreserving_measurableEquiv, MeasurePreserving.restrict_preimage_emb, volume_measurePreserving_sumPiEquivProdPi, volume_preserving_piEquivPiSubtypeProd, Ergodic.mem_extremePoints, Real.volume_preserving_transvectionStruct, volume_measurePreserving_sumPiEquivProdPi_symm, measurePreserving_div_prod, volume_preserving_funUnique, IsFundamentalDomain.measurePreserving_quotient_mk, measurePreserving_prod_neg_add_swap, measurePreserving_add_prod_neg, measurePreserving_sumPiEquivProdPi, MeasurableEquiv.measurePreserving_symm, measurePreserving_sub_prod, measurePreserving_prod_mul_right, MeasurePreserving.trans, measurePreserving_fst

Theorems

NameKindAssumesProvesValidatesDepends On
measurePreserving_subtype_coe πŸ“–mathematicalMeasurableSetMeasurePreserving
Set
Set.instMembership
Subtype.instMeasurableSpace
Measure.comap
Measure.restrict
β€”measurable_subtype_coe
map_comap_subtype_coe

MeasureTheory.MeasurableEquiv

Theorems

NameKindAssumesProvesValidatesDepends On
measurePreserving_symm πŸ“–mathematicalβ€”MeasureTheory.MeasurePreserving
DFunLike.coe
MeasurableEquiv
EquivLike.toFunLike
MeasurableEquiv.instEquivLike
MeasurableEquiv.symm
MeasureTheory.Measure.map
β€”MeasureTheory.MeasurePreserving.symm
Measurable.measurePreserving
MeasurableEquiv.measurable

MeasureTheory.MeasurePreserving

Theorems

NameKindAssumesProvesValidatesDepends On
add_measure πŸ“–mathematicalMeasureTheory.MeasurePreservingMeasureTheory.MeasurePreserving
MeasureTheory.Measure
MeasureTheory.Measure.instAdd
β€”measurable
MeasureTheory.Measure.map_add
map_eq
aeconst_comp πŸ“–mathematicalMeasureTheory.MeasurePreserving
MeasureTheory.NullMeasurable
Filter.EventuallyConst
MeasureTheory.ae
MeasureTheory.Measure
MeasureTheory.Measure.instFunLike
MeasureTheory.Measure.instOuterMeasureClass
β€”MeasureTheory.Measure.instOuterMeasureClass
measure_preimage
MeasureTheory.NullMeasurableSet.compl
Set.Subsingleton.measurableSet
aeconst_preimage πŸ“–mathematicalMeasureTheory.MeasurePreserving
MeasureTheory.NullMeasurableSet
Filter.EventuallyConst
Set.preimage
MeasureTheory.ae
MeasureTheory.Measure
MeasureTheory.Measure.instFunLike
MeasureTheory.Measure.instOuterMeasureClass
β€”aeconst_comp
Prop.instMeasurableSingletonClass
MeasurableSet.mem
aemeasurable πŸ“–mathematicalMeasureTheory.MeasurePreservingAEMeasurableβ€”Measurable.aemeasurable
measurable
aemeasurable_comp_iff πŸ“–mathematicalMeasureTheory.MeasurePreserving
MeasurableEmbedding
AEMeasurableβ€”map_eq
MeasurableEmbedding.aemeasurable_map_iff
comp πŸ“–mathematicalMeasureTheory.MeasurePreservingMeasureTheory.MeasurePreservingβ€”Measurable.comp
measurable
MeasureTheory.Measure.map_map
map_eq
comp_left_iff πŸ“–mathematicalMeasureTheory.MeasurePreserving
DFunLike.coe
MeasurableEquiv
EquivLike.toFunLike
MeasurableEquiv.instEquivLike
MeasureTheory.MeasurePreserving
DFunLike.coe
MeasurableEquiv
EquivLike.toFunLike
MeasurableEquiv.instEquivLike
β€”MeasurableEquiv.symm_comp_self
CompTriple.comp_eq
CompTriple.instId_comp
CompTriple.instIsIdId
comp
symm
comp_right_iff πŸ“–mathematicalMeasureTheory.MeasurePreserving
DFunLike.coe
MeasurableEquiv
EquivLike.toFunLike
MeasurableEquiv.instEquivLike
MeasureTheory.MeasurePreserving
DFunLike.coe
MeasurableEquiv
EquivLike.toFunLike
MeasurableEquiv.instEquivLike
β€”MeasurableEquiv.self_comp_symm
CompTriple.comp_eq
CompTriple.instComp_id
CompTriple.instIsIdId
comp
symm
exists_mem_iterate_mem πŸ“–mathematicalMeasureTheory.MeasurePreserving
MeasureTheory.NullMeasurableSet
Set
Set.instMembership
Nat.iterate
β€”ENNReal.exists_nat_mul_gt
MeasureTheory.measure_ne_top
exists_mem_iterate_mem_of_measure_univ_lt_mul_measure
LT.lt.ne'
exists_mem_iterate_mem_of_measure_univ_lt_mul_measure πŸ“–mathematicalMeasureTheory.MeasurePreserving
MeasureTheory.NullMeasurableSet
ENNReal
Preorder.toLT
PartialOrder.toPreorder
ENNReal.instPartialOrder
DFunLike.coe
MeasureTheory.Measure
Set
MeasureTheory.Measure.instFunLike
Set.univ
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
ENNReal.instCommSemiring
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
instAddCommMonoidWithOneENNReal
Set
Set.instMembership
Set.Ioo
Nat.instPreorder
Nat.iterate
β€”MeasureTheory.NullMeasurableSet.preimage
quasiMeasurePreserving
iterate
measure_preimage
Finset.sum_congr
Finset.sum_const
Finset.card_range
nsmul_eq_mul
MeasureTheory.exists_nonempty_inter_of_measure_univ_lt_sum_measure
tsub_pos_of_lt
Nat.instCanonicallyOrderedAdd
Nat.instOrderedSub
lt_of_le_of_lt
Function.iterate_add_apply
tsub_add_cancel_of_le
CanonicallyOrderedAdd.toExistsAddOfLE
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
LT.lt.le
Ne.lt_or_gt
id πŸ“–mathematicalβ€”MeasureTheory.MeasurePreservingβ€”measurable_id
MeasureTheory.Measure.map_id
iterate πŸ“–mathematicalMeasureTheory.MeasurePreservingMeasureTheory.MeasurePreserving
Nat.iterate
β€”id
comp
map_eq πŸ“–mathematicalMeasureTheory.MeasurePreservingMeasureTheory.Measure.mapβ€”β€”
map_of_comp πŸ“–mathematicalMeasureTheory.MeasurePreserving
Measurable
MeasureTheory.MeasurePreserving
MeasureTheory.Measure.map
β€”MeasureTheory.Measure.map_map
map_eq
measurable πŸ“–mathematicalMeasureTheory.MeasurePreservingMeasurableβ€”β€”
measureReal_preimage πŸ“–mathematicalMeasureTheory.MeasurePreserving
MeasureTheory.NullMeasurableSet
MeasureTheory.Measure.real
Set.preimage
β€”measure_preimage
measure_preimage πŸ“–mathematicalMeasureTheory.MeasurePreserving
MeasureTheory.NullMeasurableSet
DFunLike.coe
MeasureTheory.Measure
Set
ENNReal
MeasureTheory.Measure.instFunLike
Set.preimage
β€”map_eq
MeasureTheory.Measure.map_applyβ‚€
Measurable.aemeasurable
measurable
measure_preimage_emb πŸ“–mathematicalMeasureTheory.MeasurePreserving
MeasurableEmbedding
DFunLike.coe
MeasureTheory.Measure
Set
ENNReal
MeasureTheory.Measure.instFunLike
Set.preimage
β€”map_eq
MeasurableEmbedding.map_apply
measure_preimage_equiv πŸ“–mathematicalMeasureTheory.MeasurePreserving
DFunLike.coe
MeasurableEquiv
EquivLike.toFunLike
MeasurableEquiv.instEquivLike
DFunLike.coe
MeasureTheory.Measure
Set
ENNReal
MeasureTheory.Measure.instFunLike
Set.preimage
MeasurableEquiv
EquivLike.toFunLike
MeasurableEquiv.instEquivLike
β€”measure_preimage_emb
MeasurableEquiv.measurableEmbedding
measure_preimage_le πŸ“–mathematicalMeasureTheory.MeasurePreservingENNReal
Preorder.toLE
PartialOrder.toPreorder
ENNReal.instPartialOrder
DFunLike.coe
MeasureTheory.Measure
Set
MeasureTheory.Measure.instFunLike
Set.preimage
β€”map_eq
MeasureTheory.Measure.le_map_apply
aemeasurable
measure_symmDiff_preimage_iterate_le πŸ“–mathematicalMeasureTheory.MeasurePreserving
MeasureTheory.NullMeasurableSet
ENNReal
Preorder.toLE
PartialOrder.toPreorder
ENNReal.instPartialOrder
DFunLike.coe
MeasureTheory.Measure
Set
MeasureTheory.Measure.instFunLike
symmDiff
SemilatticeSup.toMax
Lattice.toSemilatticeSup
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
Set.instSDiff
Set.preimage
Nat.iterate
AddMonoid.toNSMul
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
instAddCommMonoidWithOneENNReal
β€”symmDiff_self
MeasureTheory.measure_empty
MeasureTheory.Measure.instOuterMeasureClass
zero_nsmul
instReflLe
add_smul
one_smul
le_imp_le_of_le_of_le
le_refl
add_le_add_left
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
ENNReal.instIsOrderedAddMonoid
MeasureTheory.measure_symmDiff_le
MeasureTheory.NullMeasurableSet.symmDiff
MeasureTheory.NullMeasurableSet.preimage
quasiMeasurePreserving
Function.iterate_succ'
Set.preimage_comp
Set.preimage_symmDiff
measure_preimage
iterate
of_isEmpty πŸ“–mathematicalβ€”MeasureTheory.MeasurePreservingβ€”measurable_of_subsingleton_codomain
IsEmpty.instSubsingleton
MeasureTheory.Measure.instSubsingleton
of_semiconj πŸ“–mathematicalMeasureTheory.MeasurePreserving
Function.Semiconj
Measurable
MeasureTheory.MeasurePreservingβ€”map_of_comp
comp
Function.Semiconj.comp_eq
measurable
map_eq
preimage_null πŸ“–mathematicalMeasureTheory.MeasurePreserving
DFunLike.coe
MeasureTheory.Measure
Set
ENNReal
MeasureTheory.Measure.instFunLike
instZeroENNReal
DFunLike.coe
MeasureTheory.Measure
Set
ENNReal
MeasureTheory.Measure.instFunLike
Set.preimage
instZeroENNReal
β€”MeasureTheory.Measure.QuasiMeasurePreserving.preimage_null
quasiMeasurePreserving
quasiMeasurePreserving πŸ“–mathematicalMeasureTheory.MeasurePreservingMeasureTheory.Measure.QuasiMeasurePreservingβ€”measurable
Eq.absolutelyContinuous
map_eq
restrict_image_emb πŸ“–mathematicalMeasureTheory.MeasurePreserving
MeasurableEmbedding
MeasureTheory.MeasurePreserving
MeasureTheory.Measure.restrict
Set.image
β€”Set.preimage_image_eq
MeasurableEmbedding.injective
restrict_preimage_emb
restrict_preimage πŸ“–mathematicalMeasureTheory.MeasurePreserving
MeasurableSet
MeasureTheory.MeasurePreserving
MeasureTheory.Measure.restrict
Set.preimage
β€”measurable
map_eq
MeasureTheory.Measure.restrict_map
restrict_preimage_emb πŸ“–mathematicalMeasureTheory.MeasurePreserving
MeasurableEmbedding
MeasureTheory.MeasurePreserving
MeasureTheory.Measure.restrict
Set.preimage
β€”measurable
map_eq
MeasurableEmbedding.restrict_map
sfinite πŸ“–mathematicalMeasureTheory.MeasurePreservingMeasureTheory.SFiniteβ€”map_eq
MeasureTheory.Measure.instSFiniteMap
sigmaFinite πŸ“–mathematicalMeasureTheory.MeasurePreservingMeasureTheory.SigmaFiniteβ€”MeasureTheory.SigmaFinite.of_map
aemeasurable
map_eq
smul_measure πŸ“–mathematicalMeasureTheory.MeasurePreservingMeasureTheory.MeasurePreserving
MeasureTheory.Measure
MeasureTheory.Measure.instSMul
β€”measurable
MeasureTheory.Measure.map_smul
map_eq
trans πŸ“–mathematicalMeasureTheory.MeasurePreserving
DFunLike.coe
MeasurableEquiv
EquivLike.toFunLike
MeasurableEquiv.instEquivLike
MeasureTheory.MeasurePreserving
DFunLike.coe
MeasurableEquiv
EquivLike.toFunLike
MeasurableEquiv.instEquivLike
MeasurableEquiv.trans
β€”comp

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