[EtienneC30]

If X is a right-continuous strongly adapted stochastic process, then it is strongly measurable when seen as a path-valued random variable.

---

• depends on: [Merged by Bors] - feat: define càdlàg functions #43352
• depends on: [Merged by Bors] - feat: tag Function.leftLim with to_dual #43525
• depends on: [Merged by Bors] - feat: use IsApply for SimpleFunc #45077

Co-authored-by: @RemyDegenne

[github-actions]

PR summary f0dfd6b009

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Probability.Process.StronglyMeasurablePath (new file)	2953

---

Declarations diff (regex)

+ Dense.nhdsWithin_inter_neBot
+ StronglyAdapted.stronglyMeasurable_path_of_isRightContinuous
+ isSeparable_iUnion_range_of_stronglyMeasurable_of_isRightContinuous
+ pathApproxRight
+ pathApproxRight_apply
+ pathApproxRight_apply_of_isLeast
+ stronglyMeasurable_path_of_isRightContinuous

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 f0dfd6b).

• +8 new declarations
• −0 removed declarations

+Dense.nhdsWithin_inter_neBot
+MeasureTheory.StronglyAdapted.stronglyMeasurable_path_of_isLeftContinuous
+MeasureTheory.StronglyAdapted.stronglyMeasurable_path_of_isRightContinuous
+MeasureTheory.isSeparable_iUnion_range_of_stronglyMeasurable_of_isLeftContinuous
+MeasureTheory.isSeparable_iUnion_range_of_stronglyMeasurable_of_isRightContinuous
+MeasureTheory.stronglyMeasurable_path_of_isLeftContinuous
+MeasureTheory.stronglyMeasurable_path_of_isRightContinuous
+Set.enumerateCountable.congr_simp

---

No changes to strong technical debt.
No changes to weak technical debt.

Current commit f0dfd6b009
Reference commit c31114ff81

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.py 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:

• [Merged by Bors] - feat: define càdlàg functions #43352
• [Merged by Bors] - feat: tag Function.leftLim with to_dual #43525
• [Merged by Bors] - feat: use IsApply for SimpleFunc #45077
  By Dependent Issues (🤖). Happy coding!