Theorems · Theorem · probability

ProbabilityTheory.Kernel.exists_ae_eq_isMarkovKernel

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {κ : ProbabilityTheory.Kernel α β}
  {μ : MeasureTheory.Measure α},
  (∀ᵐ (a : α) ∂μ, MeasureTheory.IsProbabilityMeasure (κ a)) →
    μ ≠ 0 → ∃ η, ⇑κ =ᵐ[μ] ⇑η ∧ ProbabilityTheory.IsMarkovKernel η

Defined in: Mathlib.Probability.Kernel.Basic
Cited by: 6 results in Mathlib
Foundations: Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites26

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

DFunLike.coestatement and proof · cited by 62,936
Setproof · cited by 53,352
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
Set.ofPredproof · cited by 6,101
Set.univproof · cited by 3,945
Filter.Eventuallystatement and proof · cited by 3,134
MeasurableSetproof · cited by 3,075
Compl.complproof · cited by 2,925
add_zeroproof · cited by 2,707
MeasureTheory.aestatement and proof · cited by 2,352
Filter.EventuallyEqstatement · cited by 1,912

Cited by6

Results whose statement or proof uses this declaration.

ProbabilityTheory.Kernel.iIndepFun.indepFun_finsetproof · cited by 8
ProbabilityTheory.Kernel.iIndepSets.iIndepproof · cited by 4
ProbabilityTheory.Kernel.iIndepSet.indep_generateFrom_of_disjointproof · cited by 4
ProbabilityTheory.Kernel.indep_iSup_directed_limsupproof · cited by 3
ProbabilityTheory.Kernel.indep_iSup_of_disjointproof · cited by 3
ProbabilityTheory.Kernel.iIndepFun.iIndepFun_processproof · cited by 2