feat: the product of vector measures

[sgouezel]

---

[github-actions]

PR summary 83058d3e90

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.MeasureTheory.VectorMeasure.Prod (new file)	2407

---

Declarations diff (regex)

+ HasProd
+ HasProd.flip
+ ext_of_generateFrom
+ hasProd_flip_iff
+ instance [CompleteSpace G] [IsFiniteMeasure μ.variation] : HasProd μ ν B
+ instance [CompleteSpace G] [IsFiniteMeasure μ.variation] [IsFiniteMeasure ν.variation] :
+ instance [CompleteSpace G] [h : IsFiniteMeasure ν.variation] : HasProd μ ν B
+ integrable_vectorMeasure_prodMk_left
+ of_biUnion
+ of_if
+ prod
+ prodOfIsFiniteMeasureLeft
+ prod_apply
+ prod_apply_eq_integral
+ prod_eq_of_forall_apply_prod
+ prod_eq_zero_of_not_hasProd
+ prod_flip_apply_eq_integral
+ restrict_apply_univ
+ stronglyMeasurable_vectorMeasure_prodMk_left
+ variation_prod_le

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 -- unavailable)

⚠️ The Mathlib cache for this PR's merge-base isn't on the server (typically a bors-batch intermediate that CI never built). Merge master into this PR and push to refresh.

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit 83058d3e90
Reference commit e3b73828b0

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 Formatted Correctly

The title of this PR has been updated to match our commit style conventions.
Thank you!