[Merged by Bors] - feat(Probability): notation and lemmas for the composition of a measure and a kernel (Measure.bind)

[RemyDegenne]

From the TestingLowerBounds project.
Co-authored-by: Lorenzo Luccioli

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• depends on: [Merged by Bors] - feat(Probability): parallel composition of kernels #19482

[github-actions]

PR summary afeec6a9e6

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Probability.Kernel.Proper	1
Mathlib.Probability.Kernel.Composition.CompNotation (new file)	1403
Mathlib.Probability.Kernel.Composition.MeasureComp (new file)	2001
Mathlib.Probability.Kernel.Composition.Lemmas (new file)	2003

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Declarations diff

+ AbsolutelyContinuous.comp
+ AbsolutelyContinuous.comp_left
+ AbsolutelyContinuous.comp_right
+ IsProper.setLIntegral_eq_comp
+ MeasureTheory.Measure.parallelComp_comp_compProd
+ add_comp
+ add_comp'
+ compProd_eq_comp_prod
+ compProd_eq_parallelComp_comp_copy_comp
+ compProd_id
+ compProd_id_eq_copy_comp
+ comp_add
+ comp_apply_univ
+ comp_assoc
+ comp_smul
+ const_comp
+ deterministic_comp_eq_map
+ fst.instIsZeroOrProbabilityMeasure
+ id_comp
+ instance [IsFiniteMeasure μ] [IsFiniteKernel κ] : IsFiniteMeasure (κ ∘ₘ μ) := by
+ instance [IsProbabilityMeasure μ] [IsMarkovKernel κ] : IsProbabilityMeasure (κ ∘ₘ μ) := by
+ instance [SFinite μ] [IsSFiniteKernel κ] : SFinite (κ ∘ₘ μ) := by
+ map_comp
+ parallelComp_comm
+ parallelComp_comp_parallelComp
+ parallelComp_comp_prod
+ parallelComp_id_left_comp_parallelComp
+ parallelComp_id_right_comp_parallelComp
+ prod_comp_left
+ prod_comp_right
+ snd.instIsZeroOrProbabilityMeasure
+ snd_compProd
+ swap_comp
++ instance [IsZeroOrProbabilityMeasure μ] [IsZeroOrMarkovKernel κ] :

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.

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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).

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• [Merged by Bors] - feat(Probability): parallel composition of kernels #19482
  By Dependent Issues (🤖). Happy coding!

[sgouezel]

LGTM, thanks!

[RemyDegenne]

I created a new file for the notation to be able to import it elsewhere more easily.

[RemyDegenne]

lake exe shake was not happy because the Proper file imported CompNotation only for a notation, so I ran lake exe shake --update to add an exception.

[sgouezel]

bors d+
Thanks!

[mathlib-bors]

✌️ RemyDegenne can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[RemyDegenne]

bors r+

[mathlib-bors]

Pull request successfully merged into master.

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