chore(MeasureTheory): generalize hypotheses to NullMeasurableSet

[D-Thomine]

This PR generalizes many statements in Mathlib.MeasureTheory from MeasurableSet s to NullMeasurableSet s μ.

This is particularly useful for lemmas around uniform integrability. A few technical statements which existed only to work around issues of measurability are deprecated thanks to this: MemLp.eLpNorm_indicator_le_of_meas, UniformIntegrable.spec', MemLp.uniformIntegrable_of_identDistrib_aux. This PR is a preliminary (and necessary) work before a much more thorough refactor of MeasureTheory.Function.UniformIntegrable.

I have chosen to change the hypotheses in place (generalizing the lemmas) instead of adding variants with the new hypothesis, in order to limit quasi-duplicates. There are some limits to this strategy, and a few lemmas have now both MeasurableSet and NullMeasurableSet versions:

• either if the MeasurableSet version was tagged as simp;
• or integrable_indicator_iff₀, setLIntegral_congr_fun_ae₀, setLIntegral_congr_fun₀, setLIntegral_eq_zero₀, lintegral_add_compl₀, setLIntegral_compl₀.

The latter 6 lemmas account for the largest potential downstream effects of this PR. If I did not keep the former versions of these 6 lemmas, this PR would have affected five time as many files, including files in e.g. Geometry or NumberTheory. It seems reasonable that, for quality of life purposes, we keep a few files with MeasurableSet hypotheses which are widely used in settings where measurability is essentially a given.

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[github-actions]

PR summary 41781a779e

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff (regex)

+ ae_restrict_eq₀
+ integrable_indicator_iff₀
+ le_eLpNorm_of_bddBelow'
+ lintegral_add_compl₀
+ restrict_add_restrict_compl₀
+ setLIntegral_compl₀
+ setLIntegral_congr_fun_ae₀
+ setLIntegral_congr_fun₀
+ setLIntegral_eq_zero₀

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit 41781a7).

• +9 new declarations
• −0 removed declarations

+MeasureTheory.Measure.restrict_add_restrict_compl₀
+MeasureTheory.ae_restrict_eq₀
+MeasureTheory.integrable_indicator_iff₀
+MeasureTheory.le_eLpNorm_of_bddBelow'
+MeasureTheory.lintegral_add_compl₀
+MeasureTheory.setLIntegral_compl₀
+MeasureTheory.setLIntegral_congr_fun_ae₀
+MeasureTheory.setLIntegral_congr_fun₀
+MeasureTheory.setLIntegral_eq_zero₀

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit 41781a779e
Reference commit 4ac22c7efc

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/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).

[felixpernegger]

FYI I also have #42406 open (though i need to fix some stuff);

for this PR this is not a big issue, but later it will probably be a wise idea to have multiple large scale refactors around the same files open simultaneously :)

[felixpernegger]

You should depcrecate the old name (in case you didnt, maybe i overlooked it)

[felixpernegger]

I think it would help to split this PR up in slightly smaller pieces (unless this causes big annoyances)

I.e. first PR for the lemmas you need, second for Measurable => AEMeasurable and third for MeasurableSet => NullMeasurable or whatever

This would make reviewing somewhat easier