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chore(MeasureTheory): remove the dependence of the Lebesgue decomposition on Bochner integrals#19278

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RemyDegenne wants to merge 18 commits intomasterfrom
RD_exhaustion
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chore(MeasureTheory): remove the dependence of the Lebesgue decomposition on Bochner integrals#19278
RemyDegenne wants to merge 18 commits intomasterfrom
RD_exhaustion

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@RemyDegenne RemyDegenne commented Nov 20, 2024

WIP. This PR has become a huge mess. I will open other PRs for the useful parts and then close it.


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@RemyDegenne RemyDegenne added WIP Work in progress t-measure-probability Measure theory / Probability theory labels Nov 20, 2024
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PR summary 15186c2643

Import changes for modified files

Dependency changes

File Base Count Head Count Change
Mathlib.Probability.Kernel.Composition 1931 1344 -587 (-30.40%)
Mathlib.MeasureTheory.Decomposition.RadonNikodym 1905 1384 -521 (-27.35%)
Mathlib.MeasureTheory.Decomposition.Lebesgue 1900 1383 -517 (-27.21%)
Mathlib.Probability.Kernel.WithDensity 1931 1881 -50 (-2.59%)
Mathlib.MeasureTheory.Measure.Tilted 1906 1898 -8 (-0.42%)
Import changes for all files
Files Import difference
Mathlib.Probability.Kernel.Composition Mathlib.Probability.Kernel.Invariance -587
Mathlib.MeasureTheory.Decomposition.RadonNikodym -521
Mathlib.MeasureTheory.Measure.WithDensityFinite -520
Mathlib.MeasureTheory.Decomposition.Lebesgue -517
Mathlib.Probability.Kernel.WithDensity -50
Mathlib.Probability.Kernel.Disintegration.CondCDF Mathlib.Probability.CDF -34
Mathlib.Probability.Kernel.Disintegration.CDFToKernel -31
Mathlib.Probability.Kernel.RadonNikodym Mathlib.Probability.Kernel.Disintegration.Density -21
4 files Mathlib.MeasureTheory.Covering.LiminfLimsup Mathlib.MeasureTheory.Covering.DensityTheorem Mathlib.MeasureTheory.Covering.Differentiation Mathlib.MeasureTheory.Covering.Besicovitch
-19
Mathlib.MeasureTheory.Measure.LogLikelihoodRatio Mathlib.MeasureTheory.Measure.Tilted -8
11 files Mathlib.Dynamics.Ergodic.AddCircle Mathlib.Analysis.Calculus.BumpFunction.Convolution Mathlib.Analysis.SpecialFunctions.PolarCoord Mathlib.MeasureTheory.Order.UpperLower Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace Mathlib.MeasureTheory.Covering.OneDim Mathlib.MeasureTheory.Function.Jacobian Mathlib.Analysis.ConstantSpeed Mathlib.Analysis.Calculus.Monotone Mathlib.Analysis.BoundedVariation Mathlib.NumberTheory.WellApproximable
-4
53 files Mathlib.NumberTheory.LSeries.HurwitzZetaValues Mathlib.Analysis.SpecialFunctions.Gamma.Basic Mathlib.NumberTheory.Harmonic.ZetaAsymp Mathlib.Analysis.Fourier.PoissonSummation Mathlib.NumberTheory.NumberField.Discriminant.Basic Mathlib.Analysis.Distribution.FourierSchwartz Mathlib.NumberTheory.EulerProduct.DirichletLSeries Mathlib.NumberTheory.LSeries.DirichletContinuation Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral Mathlib.Analysis.SpecialFunctions.Gamma.Beta Mathlib.Analysis.FunctionalSpaces.SobolevInequality Mathlib.NumberTheory.LSeries.ZMod Mathlib.Probability.Distributions.Exponential Mathlib.Analysis.SpecialFunctions.ImproperIntegrals Mathlib.Analysis.SpecialFunctions.Gamma.Deligne Mathlib.NumberTheory.ModularForms.JacobiTheta.Manifold Mathlib.MeasureTheory.Measure.Lebesgue.VolumeOfBalls Mathlib.NumberTheory.Cyclotomic.Three Mathlib.NumberTheory.LSeries.HurwitzZetaEven Mathlib.Analysis.SpecialFunctions.Gaussian.PoissonSummation Mathlib.Analysis.Fourier.Inversion Mathlib.NumberTheory.Harmonic.GammaDeriv Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone Mathlib.NumberTheory.ModularForms.JacobiTheta.OneVariable Mathlib.Analysis.Fourier.FourierTransformDeriv Mathlib.NumberTheory.LSeries.RiemannZeta Mathlib.NumberTheory.FLT.Three Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody Mathlib.NumberTheory.ModularForms.JacobiTheta.Bounds Mathlib.NumberTheory.LSeries.Dirichlet Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable Mathlib.NumberTheory.LSeries.Nonvanishing Mathlib.MeasureTheory.Integral.IntegralEqImproper Mathlib.NumberTheory.LSeries.MellinEqDirichlet Mathlib.NumberTheory.Cyclotomic.PID Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup Mathlib.MeasureTheory.Integral.PeakFunction Mathlib.NumberTheory.NumberField.Units.DirichletTheorem Mathlib.MeasureTheory.Integral.ExpDecay Mathlib.NumberTheory.NumberField.Units.Regulator Mathlib.Analysis.MellinInversion Mathlib.NumberTheory.LSeries.HurwitzZetaOdd Mathlib.Analysis.Calculus.LineDeriv.IntegrationByParts Mathlib.Probability.Distributions.Pareto Mathlib.Analysis.MellinTransform Mathlib.MeasureTheory.Integral.Gamma Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd Mathlib.Probability.Distributions.Gamma Mathlib.NumberTheory.NumberField.ClassNumber Mathlib.NumberTheory.LSeries.HurwitzZeta Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform Mathlib.Analysis.SpecialFunctions.Gamma.Deriv Mathlib.NumberTheory.LSeries.AbstractFuncEq
-1
148 files Mathlib.MeasureTheory.Integral.VitaliCaratheodory Mathlib.Analysis.CStarAlgebra.GelfandDuality Mathlib.Analysis.SpecialFunctions.Integrals Mathlib.MeasureTheory.Measure.FiniteMeasure Mathlib.MeasureTheory.Integral.IntervalAverage Mathlib.Analysis.Calculus.ParametricIntervalIntegral Mathlib.MeasureTheory.Measure.ProbabilityMeasure Mathlib.MeasureTheory.Function.UnifTight Mathlib.NumberTheory.GaussSum Mathlib.MeasureTheory.Integral.IntervalIntegral Mathlib.Analysis.Complex.AbsMax Mathlib.Analysis.CStarAlgebra.Spectrum Mathlib.Geometry.Manifold.Complex Mathlib.MeasureTheory.Integral.CircleIntegral Mathlib.MeasureTheory.Integral.TorusIntegral Mathlib.MeasureTheory.Function.L2Space Mathlib.MeasureTheory.Measure.LevyProkhorovMetric Mathlib.Algebra.Module.ZLattice.Covolume Mathlib.MeasureTheory.Function.ContinuousMapDense Mathlib.Analysis.Complex.Periodic Mathlib.Analysis.Complex.TaylorSeries Mathlib.Analysis.Normed.Algebra.Spectrum Mathlib.Analysis.CStarAlgebra.Module.Constructions Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric Mathlib.Analysis.SpecialFunctions.Complex.Arctan Mathlib.MeasureTheory.Function.SimpleFuncDenseLp Mathlib.MeasureTheory.Integral.DivergenceTheorem Mathlib.NumberTheory.NumberField.EquivReindex Mathlib.Analysis.Fourier.ZMod Mathlib.Analysis.SpecialFunctions.Complex.LogBounds Mathlib.Analysis.Complex.PhragmenLindelof Mathlib.Algebra.Module.ZLattice.Basic Mathlib.MeasureTheory.Integral.FundThmCalculus Mathlib.MeasureTheory.Measure.Portmanteau Mathlib.NumberTheory.LSeries.Deriv Mathlib.MeasureTheory.Measure.Haar.NormedSpace Mathlib.Analysis.Fourier.AddCircle Mathlib.NumberTheory.NumberField.Completion Mathlib.Analysis.SpecialFunctions.NonIntegrable Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable Mathlib.MeasureTheory.Group.AddCircle Mathlib.Analysis.SpecialFunctions.Complex.Analytic Mathlib.NumberTheory.ModularForms.EisensteinSeries.Basic Mathlib.MeasureTheory.Function.UniformIntegrable Mathlib.MeasureTheory.Integral.Bochner Mathlib.MeasureTheory.Measure.Haar.Unique Mathlib.Geometry.Manifold.BumpFunction Mathlib.Data.Real.Pi.Irrational Mathlib.Analysis.Complex.CauchyIntegral Mathlib.MeasureTheory.Group.GeometryOfNumbers Mathlib.Analysis.Calculus.ParametricIntegral Mathlib.MeasureTheory.Function.AEEqFun.DomAct Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic Mathlib.MeasureTheory.Integral.Prod Mathlib.NumberTheory.Cyclotomic.Embeddings Mathlib.MeasureTheory.Integral.Layercake Mathlib.Analysis.CStarAlgebra.Module.Defs Mathlib.Analysis.Complex.Schwarz Mathlib.Data.Real.Pi.Leibniz Mathlib.NumberTheory.NumberField.Units.Basic Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Integral Mathlib.MeasureTheory.Integral.LebesgueNormedSpace Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique Mathlib.NumberTheory.DirichletCharacter.GaussSum Mathlib.MeasureTheory.Measure.FiniteMeasureProd Mathlib.NumberTheory.ModularForms.EisensteinSeries.MDifferentiable Mathlib.NumberTheory.Fermat Mathlib.MeasureTheory.Integral.Asymptotics Mathlib.Analysis.CStarAlgebra.ApproximateUnit Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog Mathlib.Tactic.NormNum.LegendreSymbol Mathlib.Analysis.Fourier.RiemannLebesgueLemma Mathlib.Analysis.BoxIntegral.Integrability Mathlib.MeasureTheory.Function.StronglyMeasurable.Lp Mathlib.Analysis.Complex.Polynomial.Basic Mathlib.MeasureTheory.Function.LpSpace.ContinuousCompMeasurePreserving Mathlib.MeasureTheory.Function.L1Space Mathlib.Analysis.Complex.RemovableSingularity Mathlib.Analysis.Complex.Liouville Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.GaussSum Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol Mathlib.Analysis.Complex.LocallyUniformLimit Mathlib.NumberTheory.LSeries.Positivity Mathlib.NumberTheory.LegendreSymbol.AddCharacter Mathlib.NumberTheory.JacobiSum.Basic Mathlib.MeasureTheory.Group.FundamentalDomain Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity Mathlib.MeasureTheory.Function.LocallyIntegrable Mathlib.Analysis.InnerProductSpace.StarOrder Mathlib.MeasureTheory.Integral.BoundedContinuousFunction Mathlib.Analysis.Normed.Algebra.Basic Mathlib.Dynamics.Ergodic.Action.OfMinimal Mathlib.Analysis.SpecialFunctions.Stirling Mathlib.RingTheory.Polynomial.Selmer Mathlib.Analysis.SumIntegralComparisons Mathlib.MeasureTheory.Constructions.HaarToSphere Mathlib.Analysis.SpecialFunctions.JapaneseBracket Mathlib.MeasureTheory.Integral.CircleTransform Mathlib.MeasureTheory.Integral.DominatedConvergence Mathlib.NumberTheory.ZetaValues Mathlib.Analysis.Complex.Positivity Mathlib.MeasureTheory.Function.StronglyMeasurable.Lemmas Mathlib.Analysis.Fourier.FourierTransform Mathlib.Probability.Independence.Integrable Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances Mathlib.Analysis.Convolution Mathlib.Analysis.CStarAlgebra.Hom Mathlib.Analysis.Complex.Polynomial.UnitTrinomial Mathlib.Geometry.Manifold.PartitionOfUnity Mathlib.MeasureTheory.Measure.SeparableMeasure Mathlib.Analysis.Complex.Hadamard Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order Mathlib.MeasureTheory.Measure.Lebesgue.Integral Mathlib.MeasureTheory.Integral.Pi Mathlib.NumberTheory.NumberField.House Mathlib.NumberTheory.NumberField.Embeddings Mathlib.MeasureTheory.Function.Intersectivity Mathlib.MeasureTheory.Integral.Periodic Mathlib.NumberTheory.Harmonic.Bounds Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar Mathlib.MeasureTheory.Measure.DiracProba Mathlib.MeasureTheory.Integral.IntegrableOn Mathlib.MeasureTheory.Integral.SetToL1 Mathlib.MeasureTheory.Measure.WithDensity Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension Mathlib.Analysis.Complex.OpenMapping Mathlib.Probability.ProbabilityMassFunction.Integrals Mathlib.Analysis.Calculus.BumpFunction.Normed Mathlib.Analysis.ODE.PicardLindelof Mathlib.MeasureTheory.Integral.SetIntegral Mathlib.Tactic Mathlib.MeasureTheory.Function.LpSpace.DomAct.Continuous Mathlib.MeasureTheory.Group.Integral Mathlib.MeasureTheory.Measure.Haar.Disintegration Mathlib.Analysis.Distribution.SchwartzSpace Mathlib.Probability.Integration Mathlib.Analysis.SpecialFunctions.Pow.Integral Mathlib.Geometry.Manifold.WhitneyEmbedding Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic Mathlib.MeasureTheory.Integral.Average Mathlib.Probability.Kernel.Integral Mathlib.LinearAlgebra.Matrix.HermitianFunctionalCalculus Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic Mathlib.Data.Real.Pi.Wallis Mathlib.Geometry.Manifold.IntegralCurve.ExistUnique Mathlib.NumberTheory.NumberField.AdeleRing Mathlib.NumberTheory.ModularForms.QExpansion Mathlib.MeasureTheory.Measure.Haar.Quotient
1
13 files Mathlib.MeasureTheory.Function.ConditionalExpectation.Unique Mathlib.Probability.Kernel.IntegralCompProd Mathlib.MeasureTheory.Function.AEEqOfIntegral Mathlib.Analysis.Convex.Integral Mathlib.Probability.Kernel.MeasurableIntegral Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic Mathlib.Probability.Kernel.Disintegration.Basic Mathlib.Analysis.Distribution.AEEqOfIntegralContDiff Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1 Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2 Mathlib.MeasureTheory.VectorMeasure.WithDensity Mathlib.Probability.Kernel.MeasureCompProd Mathlib.MeasureTheory.Function.ConditionalExpectation.Indicator
2
8 files Mathlib.Probability.Variance Mathlib.Probability.StrongLaw Mathlib.Probability.Distributions.Gaussian Mathlib.Probability.Moments Mathlib.Probability.IdentDistrib Mathlib.Analysis.Calculus.Rademacher Mathlib.Probability.ConditionalExpectation Mathlib.Probability.Notation
3
Mathlib.MeasureTheory.Decomposition.SignedLebesgue 5
16 files Mathlib.Probability.Process.HittingTime Mathlib.Probability.BorelCantelli Mathlib.Probability.Martingale.Upcrossing Mathlib.Probability.Martingale.OptionalSampling Mathlib.Probability.Martingale.Basic Mathlib.Probability.Martingale.Convergence Mathlib.Probability.Distributions.Uniform Mathlib.Probability.Process.Stopping Mathlib.Probability.Process.Adapted Mathlib.Probability.Process.Filtration Mathlib.Probability.Martingale.OptionalStopping Mathlib.Probability.Martingale.BorelCantelli Mathlib.Probability.Density Mathlib.MeasureTheory.Function.ConditionalExpectation.Real Mathlib.Probability.Process.PartitionFiltration Mathlib.Probability.Martingale.Centering
7
7 files Mathlib.Probability.Kernel.Disintegration.Integral Mathlib.Probability.Independence.ZeroOne Mathlib.Probability.Kernel.Disintegration.StandardBorel Mathlib.Probability.Kernel.CondDistrib Mathlib.Probability.Kernel.Condexp Mathlib.Probability.Kernel.Disintegration.Unique Mathlib.Probability.Independence.Conditional
8
Mathlib.MeasureTheory.Decomposition.SigmaFiniteSet 1308
Mathlib.MeasureTheory.Decomposition.ExhaustionFun 1337
Mathlib.Probability.Kernel.MeasurableLIntegral 1341
Mathlib.MeasureTheory.Decomposition.LebesgueDecomposition 1343
Mathlib.MeasureTheory.Function.AEEqOfLIntegral 1378
Mathlib.MeasureTheory.Decomposition.IntegralRNDeriv 1898
Mathlib.MeasureTheory.Decomposition.SignedRadonNikodym 1912

Declarations diff

+ ENNReal.aefinStronglyMeasurable_of_aemeasurable
+ ENNReal.finStronglyMeasurable_of_measurable
+ Measure.funGE
+ Measure.maximalFun
+ Measure.maximalSet
+ Measure.pSetGE
+ SimpleFunc.lintegral_le_lintegral
+ SimpleFunc.measure_support_eapprox_lt_top
+ SimpleFunc.measure_support_lt_top'
+ SimpleFunc.measure_support_lt_top_of_lintegral_ne_top
+ SimpleFunc.tendsto_eapprox
+ exists_fun_lintegral_ge
+ exists_set_measure_ge
+ lintegral_funGE_ge
+ lintegral_funGE_le
+ lintegral_maximalFun
+ measurableSet_maximalSet
+ measurableSet_pSetGE
+ measurable_funGE
+ measurable_maximalFun
+ measure_maximalSet
+ measure_pSetGE_ge
+ measure_pSetGE_le
+ not_prop_of_subset_compl_maximalSet
+ prop_funGE
+ prop_maximalFun
+ prop_maximalSet
+ prop_pSetGE
+ sigmaFinite_iUnion
+ tendsto_lintegral_funGE
+ tendsto_measure_pSetGE
- Measure.sigmaFiniteSetGE
- exists_isSigmaFiniteSet_measure_ge
- measurableSet_sigmaFiniteSetGE
- measure_sigmaFiniteSetGE_ge
- measure_sigmaFiniteSetGE_le
- sigmaFinite_restrict_sigmaFiniteSetGE
- tendsto_measure_sigmaFiniteSetGE

You can run this locally as follows
## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.


Decrease in tech debt: (relative, absolute) = (1.00, 0.00)
Current number Change Type
219 -1 bare open (scoped) Classical

Current commit 15186c2643
Reference commit d6d7113602

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary
  • The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
  • The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

@leanprover-community-bot-assistant leanprover-community-bot-assistant added the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Nov 22, 2024
@RemyDegenne
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This is not useful anymore. Closing.
I made most of the meaningful changes in other PRs, and took note of the remaining ones.

@YaelDillies YaelDillies deleted the RD_exhaustion branch August 17, 2025 11:18
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