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: feat(Probability): parallel composition of kernels #19482

[github-actions]

PR summary d0c87ff25b

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Probability.Kernel.Composition.ParallelComp (new file)	1952
Mathlib.Probability.Kernel.Composition.MeasureComp (new file)	1955

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Declarations diff

+ AbsolutelyContinuous.comp
+ AbsolutelyContinuous.comp_left
+ AbsolutelyContinuous.comp_right
+ MeasureTheory.Measure.parallelComp_comp_compProd
+ MeasureTheory.Measure.prod_comp_left
+ MeasureTheory.Measure.prod_comp_right
+ compProd_eq_comp_prod
+ compProd_eq_parallelComp_comp_copy_comp
+ compProd_id
+ compProd_id_eq_copy_comp
+ comp_add_left
+ comp_add_left'
+ comp_add_right
+ comp_apply_univ
+ comp_assoc
+ comp_const
+ comp_deterministic_eq_map
+ comp_id
+ comp_smul_left
+ comp_swap
+ deterministic_comp_copy
+ instance (κ : Kernel α β) (η : Kernel γ δ) : IsSFiniteKernel (κ ∥ₖ η) := by
+ instance (κ : Kernel α β) [IsFiniteKernel κ] (η : Kernel γ δ) [IsFiniteKernel η] :
+ instance (κ : Kernel α β) [IsMarkovKernel κ] (η : Kernel γ δ) [IsMarkovKernel η] :
+ 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
+ lintegral_parallelComp
+ map_comp
+ parallelComp
+ parallelComp_apply
+ parallelComp_comm
+ parallelComp_comp_copy
+ parallelComp_comp_id_left_right
+ parallelComp_comp_id_right_left
+ parallelComp_comp_left
+ parallelComp_comp_parallelComp
+ parallelComp_comp_prod
+ parallelComp_comp_right
+ snd_compProd
+ swap_parallelComp

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:

• feat(Probability): parallel composition of kernels #19482
  By Dependent Issues (🤖). Happy coding!