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Theorems · Theorem · probability

MeasureTheory.Measure.snd_compProd

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} (μ : MeasureTheory.Measure α)
  [MeasureTheory.SFinite μ] (κ : ProbabilityTheory.Kernel α β) [ProbabilityTheory.IsSFiniteKernel κ],
  (μ.compProd κ).snd = μ.bind ⇑κ
Defined in
Mathlib.Probability.Kernel.Composition.MeasureComp
Cited by
11 results in Mathlib
Foundations
Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasureTheory.SFiniteProbabilityTheory.IsSFiniteKernel

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ProbabilityTheory.compProd_posterior_eq_map_swap · cited by 4ProbabilityTheory.compPro…ProbabilityTheory.condExpKernel_comp_trim · cited by 4ProbabilityTheory.condExp…ProbabilityTheory.Kernel.HasSubgaussianMGF.prodMkLeft_compProd · cited by 1HasSubgaussianMGF.prodMkL…MeasureTheory.Measure.prodMkLeft_comp_compProd · cited by 1Measure.prodMkLeft_comp_c…ProbabilityTheory.posterior_comp_self · cited by 1ProbabilityTheory.posteri…ProbabilityTheory.Kernel.setIntegral_traj_partialTraj · cited by 1Kernel.setIntegral_traj_p…ProbabilityTheory.HasCondDistrib.hasLaw_of_const · cited by 0HasCondDistrib.hasLaw_of_…ProbabilityTheory.condDistrib_comp_map · cited by 0ProbabilityTheory.condDis…MeasureTheory.Measure.integrable_compProd_snd_iff · cited by 0Measure.integrable_compPr…ProbabilityTheory.Kernel.integral_traj_partialTraj · cited by 0Kernel.integral_traj_part…InformationTheory.klDiv_comp_right_le · cited by 0InformationTheory.klDiv_c…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealSet.preimage · cited by 4946Set.preimageMeasurableSet · cited by 3075MeasurableSetProbabilityTheory.Kernel · cited by 1281ProbabilityTheory.KernelMeasureTheory.lintegral · cited by 1152MeasureTheory.lintegralMeasureTheory.SFinite · cited by 449MeasureTheory.SFiniteMeasureTheory.Measure.ext · cited by 308Measure.extProbabilityTheory.IsSFiniteKernel · cited by 248ProbabilityTheory.IsSFini…MeasureTheory.Measure.bind · cited by 173Measure.bindMeasureTheory.Measure.compProd · cited by 132Measure.compProdmeasurable_snd · cited by 94measurable_sndMeasure.snd_compProdCITED BYCITES

Cites20

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by11

Results whose statement or proof uses this declaration.