feat: Fubini theorem for vector measures

[sgouezel]

---

[github-actions]

PR summary 7283f985c4

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ _root_.MeasureTheory.AEStronglyMeasurable.integral_vectorMeasure_prod_right'
+ _root_.MeasureTheory.Integrable.integral_vectorMeasure_prod_left
+ _root_.MeasureTheory.Integrable.prod_vectorMeasure
+ _root_.MeasureTheory.StronglyMeasurable.integral_vectorMeasure_prod_left
+ _root_.MeasureTheory.StronglyMeasurable.integral_vectorMeasure_prod_left'
+ _root_.MeasureTheory.StronglyMeasurable.integral_vectorMeasure_prod_right
+ _root_.MeasureTheory.StronglyMeasurable.integral_vectorMeasure_prod_right'
+ continuous_integral_integral
+ integral_integral
+ integral_integral_smul
+ integral_integral_smul_swap
+ integral_integral_smul_symm
+ integral_integral_swap
+ integral_integral_symm
+ integral_prod
+ integral_prod_smul
+ integral_prod_smul_symm
+ integral_prod_swap
+ integral_prod_symm
+ lintegral_fn_integral_sub

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 7283f98).

• +20 new declarations
• −0 removed declarations

+MeasureTheory.AEStronglyMeasurable.integral_vectorMeasure_prod_right'
+MeasureTheory.Integrable.integral_vectorMeasure_prod_left
+MeasureTheory.Integrable.prod_vectorMeasure
+MeasureTheory.StronglyMeasurable.integral_vectorMeasure_prod_left
+MeasureTheory.StronglyMeasurable.integral_vectorMeasure_prod_left'
+MeasureTheory.StronglyMeasurable.integral_vectorMeasure_prod_right
+MeasureTheory.StronglyMeasurable.integral_vectorMeasure_prod_right'
+MeasureTheory.VectorMeasure.continuous_integral_integral
+MeasureTheory.VectorMeasure.integral_integral
+MeasureTheory.VectorMeasure.integral_integral_smul
+MeasureTheory.VectorMeasure.integral_integral_smul_swap
+MeasureTheory.VectorMeasure.integral_integral_smul_symm
+MeasureTheory.VectorMeasure.integral_integral_swap
+MeasureTheory.VectorMeasure.integral_integral_symm
+MeasureTheory.VectorMeasure.integral_prod
+MeasureTheory.VectorMeasure.integral_prod_smul
+MeasureTheory.VectorMeasure.integral_prod_smul_symm
+MeasureTheory.VectorMeasure.integral_prod_swap
+MeasureTheory.VectorMeasure.integral_prod_symm
+MeasureTheory.VectorMeasure.lintegral_fn_integral_sub

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit 7283f985c4
Reference commit c81c5cbb1c

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).

[github-actions]

🚨 PR Title Needs Formatting

Please update the title to match our commit style conventions.

Errors from script:

labels are []
error: the PR subject `Fubini theorem for vector measures` should be lowercased

Details on the required title format

The title should fit the following format:

<kind>(<optional-scope>): <subject>

<kind> is:

• feat (feature)
• fix (bug fix)
• doc (documentation)
• style (formatting, missing semicolons, ...)
• refactor
• test (when adding missing tests)
• chore (maintain)
• perf (performance improvement, optimization, ...)
• ci (changes to continuous integration, repo automation, ...)

<optional-scope> is a name of module or a directory which contains changed modules.
This is not necessary to include, but may be useful if the <subject> is insufficient.
The Mathlib directory prefix is always omitted.
For instance, it could be

• Data/Nat/Basic
• Algebra/Group/Defs
• Topology/Constructions

<subject> has the following constraints:

• do not capitalize the first letter
• no dot(.) at the end
• use imperative, present tense: "change" not "changed" nor "changes"

[SnirBroshi]

Hello! Could you tag the versions of Fubini's theorem with @[wikidata Q1149022]?
(https://www.wikidata.org/wiki/Q1149022)
This would list all of them under this page in the docs.

[sgouezel]

I think wikidata are not mainstream enough in Mathlib to ask for them in general PRs. Better add them later on in specific PRs (especially on this Fubini topic, as there are already several Fubini versions in Mathlib, and the tag should probably be added to all of them).

[SnirBroshi]

Umm okay, but this feels like a chicken and egg problem: they won't be maintstream until people add them in PRs such as this one. I don't mind adding them in a followup I guess.