Theorems · Theorem · probability
MeasureTheory.Measure.AbsolutelyContinuous.compProd_right
∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {μ : MeasureTheory.Measure α}
{κ η : ProbabilityTheory.Kernel α β} [MeasureTheory.SFinite μ] [ProbabilityTheory.IsSFiniteKernel η],
(∀ᵐ (a : α) ∂μ, (κ a).AbsolutelyContinuous (η a)) → (μ.compProd κ).AbsolutelyContinuous (μ.compProd η)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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.preimageproof · cited by 4,946
- Filter.Eventuallystatement and proof · cited by 3,134
- MeasurableSetproof · cited by 3,075
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
Cited by4
Results whose statement or proof uses this declaration.
- ProbabilityTheory.absolutelyContinuous_posteriorproof · cited by 4
- MeasureTheory.Measure.AbsolutelyContinuous.compProdproof · cited by 1
- ProbabilityTheory.absolutelyContinuous_of_posteriorproof · cited by 1
- MeasureTheory.Measure.absolutelyContinuous_compProd_right_iffproof · cited by 0