Theorems · Theorem · probability
ProbabilityTheory.Kernel.singularPart_eq_zero_iff_absolutelyContinuous
∀ {α : Type u_1} {γ : Type u_2} {mα : MeasurableSpace α} {mγ : MeasurableSpace γ}
[hαγ : MeasurableSpace.CountableOrCountablyGenerated α γ] (κ η : ProbabilityTheory.Kernel α γ)
[inst : ProbabilityTheory.IsFiniteKernel κ] [inst_1 : ProbabilityTheory.IsFiniteKernel η] (a : α),
(κ.singularPart η) a = 0 ↔ (κ a).AbsolutelyContinuous (η a)- Defined in
- Mathlib.Probability.Kernel.RadonNikodym
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 333 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- add_zeroproof · cited by 2,707
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- MeasureTheory.Measure.AbsolutelyContinuousstatement and proof · cited by 325
- ProbabilityTheory.IsFiniteKernelstatement and proof · cited by 178
- add_applyproof · cited by 154
- MeasurableSpace.CountableOrCountablyGeneratedstatement and proof · cited by 97
- ProbabilityTheory.Kernel.rnDerivproof · cited by 45
- ProbabilityTheory.Kernel.withDensityproof · cited by 45
- ProbabilityTheory.Kernel.singularPartstatement and proof · cited by 17
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.AbsolutelyContinuous.kernel_of_compProdproof · cited by 5
- ProbabilityTheory.Kernel.singularPart_selfproof · cited by 0