[Merged by Bors] - feat: `|∫ a, f a ∂μ| ≤ ∫ a, |f a| ∂μ` by YaelDillies · Pull Request #20540 · leanprover-community/mathlib4

YaelDillies · 2025-01-07T08:47:17Z

From LeanAPAP

github-actions · 2025-01-07T08:48:08Z

PR summary 6a574a679a

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

Declarations diff

+ abs_integral_le_integral_abs

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.

No changes to technical debt.

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).

Mathlib/MeasureTheory/Function/LpSpace.lean

RemyDegenne

This PR does two completely unrelated things (the integral lemma and the renames), but since it's so small let's say that it's fine.
Thanks!
bors r+

From LeanAPAP Moves: * `Memℒp.memℒp_of_exponent_le_of_measure_support_ne_top` -> ` Memℒp.mono_exponent_of_measure_support_ne_top` * `Memℒp.memℒp_of_exponent_le` -> ` Memℒp.mono_exponent`

mathlib-bors · 2025-01-07T10:07:17Z

Canceled.

YaelDillies · 2025-01-07T10:07:22Z

Whoops sorry I was splitting the PR

RemyDegenne · 2025-01-07T10:08:14Z

I agree a split is a good move.

…, |f a| ∂μ` From LeanAPAP

eric-wieser · 2025-01-07T20:04:16Z

Mathlib/MeasureTheory/Integral/Bochner.lean

  exact (norm_weightedSMul_le s).trans (one_mul _).symm.le

+lemma abs_integral_le_integral_abs {f : α → ℝ} : |∫ a, f a ∂μ| ≤ ∫ a, |f a| ∂μ :=
+  norm_integral_le_integral_norm f


I'm confused why you're not obliged to pass the hf that line 403 says is needed.

because you're looking at the wrong norm_integral_le_integral_norm lemma (because I put my new lemma in the wrong place). This one is SimpleFunc.norm_integral_le_integral_norm while I am using norm_integral_le_integral_norm

RemyDegenne · 2025-01-08T11:48:27Z

Thanks!
bors r+

From LeanAPAP

mathlib-bors · 2025-01-08T12:28:10Z

Pull request successfully merged into master.

Build succeeded:

* origin/master: (80 commits) chore(CategoryTheory): remove data produced by tactic block (#20565) feat: `|∫ a, f a ∂μ| ≤ ∫ a, |f a| ∂μ` (#20540) feat: the Boolean subalgebra generated by the lattice generated by a set (#20440) feat: misc. lemmas about moments, tilted measures (#20150) chore(Algebra/Lie): make IsNilpotent and IsSolvable independent of scalars (#20556) feat(Combinatorics/SimpleGraph/Path): add `IsPath.getVert_injOn` (#19373) feat(Combinatorics/SimpleGraph): add lemmas about `spanningCoe` (#19377) chore: scope 'on' notation to Function (#20562) chore: disable docPrime linter (#20559) chore: deprecate MulRingNorm._ in favour of AbsoluteValue._ (#20557) fix(scripts/bench_summary): input jobID as a Nat, rather than a String (#20539) chore: move results about `DivisionMonoid` + `HasDistribNeg` (#20551) feat(NumberTheory/NumberField/Embeddings): definition of totally real field (#20542) chore(Noetherian/Artinian): generalize to Semiring (#20534) chore: protect `Filter.nhds_{iInf,inf}` (#20530) chore(AlgebraicTopology): move SplitSimplicialObject.lean (#20511) chore: extract 3 new files out of MeasureSpace (#20509) feat(RingTheory): Jacobian criterion for smoothness of local algebras (#20326) doc(RingTheory/Flat): add reference to Lambek's paper (#20266) feat(NumberTheory/AbelSummation): add more results (#19942) chore(Multilinear/Basic): generalize the `SMul` instance (#20536) feat(FDeriv/Equiv): generalize `HasFDerivAt.of_local_left_inverse` (#20516) feat(ContDiff): add `iteratedFDeriv_comp` (#20472) feat(LowerUpperTopology): add lemmas (#20465) feat(ContDiff): weaken some assumptions (#20368) fix(scripts/technical-debt-metric): avoid division by 0 (#20537) chore(Algebra/Ring): Clean up in SumsOfSquares and Semireal/Defs (#20528) feat(FTaylorSeries): add lemmas about `dist` between 0th and 1st derivs (#20089) feat: results on inner regularity of finite measures (#19780) chore: to_additive various results on groups, group actions (#20547) feat(Probability/Kernel): `Kernel.sectL` and `sectR` (#15466) chore(CategoryTheory/Limits/Fubini): relax universes constraints and weaken hypotheses (#20553) perf: remove `@[simp]` on `Fintype.card_of{IsEmpty,Subsingleton}` (#20524) fix(HashCommandLinter): remove unnecessary, broken workaround for tests (#20529) chore(Ideal/Basic): dependent generalization of `Ideal.pi` (#20535) feat(RingTheory): being unramified is a local property (#20323) chore(BooleanSubalgebra): use `IsSublattice` in `closure_sdiff_sup_induction` (#20439) feat(Order/SuccPred/CompleteLinearOrder): `⨆ a < x, succ a = x` (#19970) chore(*): replace `no_index (ofNat n)` with `ofNat(n)` everywhere (#20521) feat(CategoryTheory/Triangulated/Adjunction): the right adjoint of a triangulated functor is triangulated (#20255) chore(Order/SuccPred/LinearLocallyFinite): change data-creating instances to defs (#20235) chore: don't import algebra in `Data.Finset.Basic` (#19779) feat: initial segment commutes with `Iio` (#20503) chore(Measure/Pi): move parts to `MeasurableSpace/` (#20215) chore: smile more often (#20436) chore(Algebra/Category/MonCat/ForgetCorepresentable, Algebra/Group/Equiv/Basic): move definitions and add symmetric version (#20416) feat(GroupTheory/QuotientGroup): group correspondence theorem (#20007) doc: change "module homomorphism" to "linear map" (#20481) perf: improves the performance of the `Repr (Equiv.Perm α)` instance (1/4) (#20519) fix: do not keep only the first line of hints (#19756) ...

eric-wieser · 2025-01-08T14:04:49Z

Mathlib/MeasureTheory/Integral/Bochner.lean

  · rw [integral_non_aestronglyMeasurable h, norm_zero]
    exact integral_nonneg_of_ae le_ae

+lemma abs_integral_le_integral_abs {f : α → ℝ} : |∫ a, f a ∂μ| ≤ ∫ a, |f a| ∂μ :=


I'd argue f should be explicit to match the lemma above.

I would rather make f implicit in the lemma above

github-actions bot added the t-measure-probability Measure theory / Probability theory label Jan 7, 2025

RemyDegenne reviewed Jan 7, 2025

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Mathlib/MeasureTheory/Function/LpSpace.lean Outdated Show resolved Hide resolved

YaelDillies changed the title ~~feat: L^p spaces of a finite measure are nested, |∫ a, f a ∂μ| ≤ ∫ a, |f a| ∂μ~~ feat: |∫ a, f a ∂μ| ≤ ∫ a, |f a| ∂μ Jan 7, 2025

RemyDegenne approved these changes Jan 7, 2025

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ghost added the ready-to-merge This PR has been sent to bors. label Jan 7, 2025

YaelDillies force-pushed the abs_integral_le_integral_abs branch from 894f798 to 1c7108d Compare January 7, 2025 10:07

RemyDegenne removed the ready-to-merge This PR has been sent to bors. label Jan 7, 2025

feat: L^p spaces of a finite measure are nested, `|∫ a, f a ∂μ| ≤ ∫ a…

b9a1836

…, |f a| ∂μ` From LeanAPAP

YaelDillies force-pushed the abs_integral_le_integral_abs branch from 1c7108d to b9a1836 Compare January 7, 2025 10:13

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fix

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ghost added the ready-to-merge This PR has been sent to bors. label Jan 8, 2025

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feat: |∫ a, f a ∂μ| ≤ ∫ a, |f a| ∂μ (#20540)

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mathlib-bors bot changed the title ~~feat: |∫ a, f a ∂μ| ≤ ∫ a, |f a| ∂μ~~ [Merged by Bors] - feat: |∫ a, f a ∂μ| ≤ ∫ a, |f a| ∂μ Jan 8, 2025

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mathlib-bors bot deleted the abs_integral_le_integral_abs branch January 8, 2025 12:28

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[Merged by Bors] - feat: `|∫ a, f a ∂μ| ≤ ∫ a, |f a| ∂μ`#20540

[Merged by Bors] - feat: `|∫ a, f a ∂μ| ≤ ∫ a, |f a| ∂μ`#20540
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PR summary 6a574a679a

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