Theorems · Theorem · probability

MeasureTheory.Measure.mutuallySingular_compProd_left_iff

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {μ ν : MeasureTheory.Measure α}
  {κ : ProbabilityTheory.Kernel α β} [MeasureTheory.SFinite μ] [MeasureTheory.SigmaFinite ν]
  [ProbabilityTheory.IsSFiniteKernel κ] [hκ : ∀ (x : α), NeZero (κ x)],
  (μ.compProd κ).MutuallySingular (ν.compProd κ) ↔ μ.MutuallySingular ν

Defined in

Mathlib.Probability.Kernel.Composition.MeasureCompProd

Cited by

0 results in Mathlib

Foundations

Depth 230 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.SFiniteMeasureTheory.SigmaFiniteProbabilityTheory.IsSFiniteKernelNeZero