Theorems · Theorem · probability

MeasureTheory.Measure.mutuallySingular_of_mutuallySingular_compProd

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {μ ν : MeasureTheory.Measure α}
  {κ η : ProbabilityTheory.Kernel α β} {ξ : MeasureTheory.Measure α} [MeasureTheory.SFinite μ] [MeasureTheory.SFinite ν]
  [ProbabilityTheory.IsSFiniteKernel κ] [ProbabilityTheory.IsSFiniteKernel η],
  (μ.compProd κ).MutuallySingular (ν.compProd η) →
    ξ.AbsolutelyContinuous μ → ξ.AbsolutelyContinuous ν → ∀ᵐ (x : α) ∂ξ, (κ x).MutuallySingular (η x)

Defined in: Mathlib.Probability.Kernel.Composition.MeasureCompProd
Cited by: 2 results in Mathlib
Foundations: Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasureTheory.SFinite MeasureTheory.SFinite ProbabilityTheory.IsSFiniteKernel ProbabilityTheory.IsSFiniteKernel

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Cites28

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
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealproof · cited by 9,879
Set.ofPredproof · cited by 6,101
Set.preimageproof · cited by 4,946
Filter.Eventuallystatement · cited by 3,134
MeasurableSetproof · cited by 3,075
Compl.complproof · cited by 2,925
MeasureTheory.aestatement · cited by 2,352
Filter.univ_mem'proof · cited by 1,672
Filter.mp_memproof · cited by 1,537

Cited by2

Results whose statement or proof uses this declaration.

MeasureTheory.Measure.mutuallySingular_compProd_left_iffproof · cited by 0
MeasureTheory.Measure.mutuallySingular_compProd_right_iffproof · cited by 0