Mathlib Map

Theorems · Inductive type · probability

MeasureTheory.Measure.IsCondKernel

{α : Type u_1} →
  {Ω : Type u_3} →
    {mα : MeasurableSpace α} →
      {mΩ : MeasurableSpace Ω} → MeasureTheory.Measure (α × Ω) → ProbabilityTheory.Kernel α Ω → Prop

A kernel ρCond is a conditional kernel for a measure ρ if it disintegrates it in the sense that ρ.fst ⊗ₘ ρCond = ρ.

Defined in
Mathlib.Probability.Kernel.Disintegration.Basic
Cited by
6 results in Mathlib
Foundations
Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

MeasureTheory.Measure.disintegrate · cited by 12Measure.disintegrateMeasureTheory.Measure.IsCondKernel.apply_of_ne_zero · cited by 2IsCondKernel.apply_of_ne_…MeasureTheory.Measure.IsCondKernel.disintegrate · cited by 1IsCondKernel.disintegrateMeasureTheory.Measure.IsCondKernel.isProbabilityMeasure · cited by 1IsCondKernel.isProbabilit…MeasureTheory.Measure.IsCondKernel.casesOn · cited by 0IsCondKernel.casesOnMeasureTheory.Measure.IsCondKernel.isMarkovKernel · cited by 0IsCondKernel.isMarkovKern…MeasureTheory.Measure.IsCondKernel.isSFiniteKernel · cited by 0IsCondKernel.isSFiniteKer…MeasureTheory.Measure.IsCondKernel.recOn · cited by 0IsCondKernel.recOnMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureProbabilityTheory.Kernel · cited by 1281ProbabilityTheory.KernelMeasure.IsCondKernelCITED BYCITES

Cites3

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

Cited by8

Results whose statement or proof uses this declaration.