feat: vector measures with density wrt vector measures

[sgouezel]

---

[github-actions]

PR summary 1cbb9fd002

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.MeasureTheory.VectorMeasure.WithDensityVec (new file)	2348

---

Declarations diff (regex)

+ _root_.MeasureTheory.Measure.variation_withDensityᵥ
+ restrict_withDensity
+ variation_WithDensity_le
+ variation_withDensity
+ variation_withDensity'
+ withDensity
+ withDensity_apply
+ withDensity_apply_univ
+ withDensity_congr
+ withDensity_zero
+ withDensity_zero_vectorMeasure

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 1cbb9fd).

• +12 new declarations
• −0 removed declarations

+MeasureTheory.Measure.variation_withDensityᵥ
+MeasureTheory.VectorMeasure.restrict_withDensity
+MeasureTheory.VectorMeasure.variation_WithDensity_le
+MeasureTheory.VectorMeasure.variation_withDensity
+MeasureTheory.VectorMeasure.variation_withDensity'
+MeasureTheory.VectorMeasure.withDensity
+MeasureTheory.VectorMeasure.withDensity_apply
+MeasureTheory.VectorMeasure.withDensity_apply_univ
+MeasureTheory.VectorMeasure.withDensity_congr
+MeasureTheory.VectorMeasure.withDensity_fun_zero
+MeasureTheory.VectorMeasure.withDensity_zero
+MeasureTheory.VectorMeasure.withDensity_zero_vectorMeasure

---

No changes to strong technical debt.

Increase in weak tech debt: (relative, absolute) = (1.00, 0.00)

Current number	Change	Type (weak)
4974	1	exposed public sections

Current commit 1cbb9fd002
Reference commit 571b8a8e54

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).