Theorems · Theorem · probability
MeasureTheory.Measure.AbsolutelyContinuous.kernel_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} [ProbabilityTheory.IsFiniteKernel κ] [ProbabilityTheory.IsFiniteKernel η]
[MeasurableSpace.CountableOrCountablyGenerated α β] [MeasureTheory.SFinite μ],
(μ.compProd κ).AbsolutelyContinuous (ν.compProd η) → ∀ᵐ (a : α) ∂μ, (κ a).AbsolutelyContinuous (η a)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 335 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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
- Filter.Eventuallystatement and proof · cited by 3,134
- 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
- Filter.Eventually.of_forallproof · cited by 526
- MeasureTheory.SFinitestatement and proof · cited by 449
- MeasureTheory.Measure.AbsolutelyContinuousstatement and proof · cited by 325
- ProbabilityTheory.IsFiniteKernelstatement and proof · cited by 178
Cited by5
Results whose statement or proof uses this declaration.
- ProbabilityTheory.absolutelyContinuous_posteriorproof · cited by 4
- ProbabilityTheory.Kernel.ae_eq_of_compProd_eqproof · cited by 3
- ProbabilityTheory.absolutelyContinuous_of_posteriorproof · cited by 1
- MeasureTheory.Measure.absolutelyContinuous_compProd_iff'proof · cited by 0
- MeasureTheory.Measure.absolutelyContinuous_compProd_right_iffproof · cited by 0