Theorems · Definition · probability

ProbabilityTheory.Kernel.mutuallySingularSet

{α : Type u_1} →
  {γ : Type u_2} →
    {mα : MeasurableSpace α} →
      {mγ : MeasurableSpace γ} →
        [hαγ : MeasurableSpace.CountableOrCountablyGenerated α γ] →
          ProbabilityTheory.Kernel α γ → ProbabilityTheory.Kernel α γ → Set (α × γ)

A set of points in α × γ related to the absolute continuity / mutual singularity of κ and η.

Defined in: Mathlib.Probability.Kernel.RadonNikodym
Cited by: 4 results in Mathlib
Foundations: Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasurableSpace.CountableOrCountablyGenerated

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

Cites6

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

Setstatement · cited by 53,352
MeasurableSpacestatement and proof · cited by 13,106
Set.ofPredproof · cited by 6,101
ProbabilityTheory.Kernelstatement and proof · cited by 1,281
MeasurableSpace.CountableOrCountablyGeneratedstatement and proof · cited by 97
ProbabilityTheory.Kernel.rnDerivAuxproof · cited by 22

Cited by4

Results whose statement or proof uses this declaration.

ProbabilityTheory.Kernel.measurableSet_mutuallySingularSetSliceproof · cited by 6
ProbabilityTheory.Kernel.measurableSet_mutuallySingularSetstatement · cited by 4
MeasureTheory.Measure.MutuallySingular.compProd_of_rightproof · cited by 3
ProbabilityTheory.Kernel.rnDeriv_eq_top_iffstatement · cited by 1