Theorems · Theorem · probability
ProbabilityTheory.Kernel.singularPart_compl_mutuallySingularSetSlice
∀ {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.IsSFiniteKernel κ] [inst_1 : ProbabilityTheory.IsSFiniteKernel η] (a : α),
((κ.singularPart η) a) (κ.mutuallySingularSetSlice η a)ᶜ = 0- Defined in
- Mathlib.Probability.Kernel.RadonNikodym
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 218 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites40
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
- Setstatement · cited by 53,352
- Realproof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Set.ofPredproof · cited by 6,101
- Compl.complstatement and proof · cited by 2,925
- one_mulproof · cited by 2,841
- MeasureTheory.aeproof · cited by 2,352
- LT.lt.leproof · cited by 2,189
- mul_assocproof · cited by 1,667
Cited by4
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.mutuallySingular_singularPartproof · cited by 6
- ProbabilityTheory.Kernel.singularPart_eq_zero_iff_apply_eq_zeroproof · cited by 1
- ProbabilityTheory.Kernel.withDensity_rnDeriv_eq_zero_iff_measure_eq_zeroproof · cited by 1