feat(Probability): Local and stable properties

[kex-y]

---

Defines local and stable properties which is useful for local martingales.

• depends on: [Merged by Bors] - feat(Probability): Right continuous filtrations #33371
• depends on: [Merged by Bors] - feat: Simple lemmas about convergence in WithTop #33374
• depends on: feat(Probability): Countable infimum of stopping times is a stopping time #33372

Co-authored-by: @RemyDegenne

[github-actions]

PR summary 656cef126e

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Probability.Process.LocalProperty (new file)	2170

---

Declarations diff

+ IsLocalizingSequence
+ IsLocalizingSequence.min
+ IsPreLocalizingSequence
+ IsStable
+ IsStable.and
+ IsStable.isStable_locally
+ Locally
+ Locally.IsLocalizingSequence
+ Locally.localSeq
+ Locally.mono
+ Locally.of_and
+ Locally.of_and_left
+ Locally.of_and_right
+ Locally.stoppedProcess
+ biInf
+ iInf
+ isLocalizingSequence_const_top
+ isLocalizingSequence_of_isPreLocalizingSequence
+ isPreLocalizingSequence_of_isLocalizingSequence
+ isPreLocalizingSequence_of_isLocalizingSequence_aux
+ isPreLocalizingSequence_of_isLocalizingSequence_aux'
+ isStoppingTime_of_measurableSet_lt_of_isRightContinuous
+ isStoppingTime_of_measurableSet_lt_of_isRightContinuous'
+ le_mkStrictMonoAux
+ locally_and
+ locally_induction
+ locally_induction₂
+ locally_locally
+ locally_of_isPreLocalizingSequence
+ locally_of_prop
+ measure_iInter_of_ae_antitone
+ mkStrictMonoAux
+ mkStrictMonoAux_strictMono

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

---

No changes to technical debt.

You can run this locally as

./scripts/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).

[kex-y]

I accidentally deleted the branch for #31148 so I opened a new pr for this

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• [Merged by Bors] - feat(Probability): Right continuous filtrations #33371
• [Merged by Bors] - feat: Simple lemmas about convergence in WithTop #33374
• feat(Probability): Countable infimum of stopping times is a stopping time #33372
  By Dependent Issues (🤖). Happy coding!

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.