Theorems · Theorem · probability

MeasureTheory.Measure.AbsolutelyContinuous.compProd_left

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

Defined in: Mathlib.Probability.Kernel.Composition.MeasureCompProd
Cited by: 5 results in Mathlib
Foundations: Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasureTheory.SFinite

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Cites18

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

DFunLike.coeproof · 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
MeasurableSetproof · cited by 3,075
ProbabilityTheory.Kernelstatement and proof · cited by 1,281
MeasureTheory.SFinitestatement and proof · cited by 449
MeasureTheory.Measure.AbsolutelyContinuousstatement and proof · cited by 325
ProbabilityTheory.IsSFiniteKernelproof · cited by 248
MeasureTheory.Measure.compProdstatement and proof · cited by 132
MeasureTheory.Measure.AbsolutelyContinuous.mkproof · cited by 38

Cited by5

Results whose statement or proof uses this declaration.

MeasureTheory.Measure.AbsolutelyContinuous.compProdproof · cited by 1
MeasureTheory.Measure.absolutelyContinuous_compProd_left_iffproof · cited by 1
MeasureTheory.Measure.absolutelyContinuous_compProd_of_compProdproof · cited by 1
MeasureTheory.Measure.AbsolutelyContinuous.mutuallySingular_compProd_iffproof · cited by 1
MeasureTheory.Measure.mutuallySingular_compProd_iffproof · cited by 0