Theorems · Theorem · probability

MeasureTheory.Measure.absolutelyContinuous_of_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} [MeasureTheory.SFinite μ] [ProbabilityTheory.IsSFiniteKernel κ]
  [h_zero : ∀ (a : α), NeZero (κ a)], (μ.compProd κ).AbsolutelyContinuous (ν.compProd η) → μ.AbsolutelyContinuous ν

Defined in: Mathlib.Probability.Kernel.Composition.MeasureCompProd
Cited by: 3 results in Mathlib
Foundations: Depth 229 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasureTheory.SFinite ProbabilityTheory.IsSFiniteKernel NeZero

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Cites25

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
ENNRealproof · cited by 9,879
Set.univproof · cited by 3,945
MeasurableSetproof · cited by 3,075
MeasureTheory.aeproof · cited by 2,352
SProd.sprodproof · cited by 1,750
MeasureTheory.Measure.restrictproof · cited by 1,646
ProbabilityTheory.Kernelstatement and proof · cited by 1,281
Filter.NeBotproof · cited by 853

Cited by3

Results whose statement or proof uses this declaration.

MeasureTheory.Measure.absolutelyContinuous_compProd_iffproof · cited by 4
MeasureTheory.Measure.absolutelyContinuous_compProd_left_iffproof · cited by 1
MeasureTheory.Measure.absolutelyContinuous_compProd_iff'proof · cited by 0