feat: the delta distribution is induced by the dirac measure

[luigi-massacci]

The title

---

• depends on: feat: classical distributions induced by a locally integrable function #41723

[luigi-massacci]

Do we want to make (1 : E -> R) into a default argument for toDistribution?

[github-actions]

PR summary bf9ca672b3

Import changes exceeding 2%

%	File
+6.07%	Mathlib.Analysis.Distribution.Distribution

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Analysis.Distribution.Distribution	2439	2587	+148 (+6.07%)

Import changes for all files

Files	Import difference
Mathlib.Analysis.Distribution.Distribution	148

---

Declarations diff (regex)

+ integrable_smul
+ toDistribution
+ toDistribution_add
+ toDistribution_apply
+ toDistribution_dirac_eq_delta
+ toDistribution_eq_of_ae
+ toDistribution_eq_zero
+ toDistribution_injective
+ toDistribution_neg
+ toDistribution_smul
+ toDistribution_zero
+ zero_on_compl

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 bf9ca67).

• +13 new declarations
• −0 removed declarations

+Distribution.toDistribution
+Distribution.toDistribution.congr_simp
+Distribution.toDistribution_add
+Distribution.toDistribution_apply
+Distribution.toDistribution_dirac_eq_delta
+Distribution.toDistribution_eq_of_ae
+Distribution.toDistribution_eq_zero
+Distribution.toDistribution_injective
+Distribution.toDistribution_neg
+Distribution.toDistribution_smul
+Distribution.toDistribution_zero
+TestFunction.integrable_smul
+TestFunction.zero_on_compl

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit bf9ca672b3
Reference commit 2eb08ab8c9

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).

[mathlib-dependent-issues]

This PR/issue depends on:

• feat: classical distributions induced by a locally integrable function #41723
  By Dependent Issues (🤖). Happy coding!