Theorems · Theorem · probability
ProbabilityTheory.Kernel.measure_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)
[ProbabilityTheory.IsFiniteKernel κ] [ProbabilityTheory.IsFiniteKernel η] (a : α),
(η a) (κ.mutuallySingularSetSlice η a) = 0- Defined in
- Mathlib.Probability.Kernel.RadonNikodym
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 329 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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
- 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
- zero_addproof · cited by 2,366
- MeasureTheory.aeproof · cited by 2,352
- MeasureTheory.Measure.restrictproof · cited by 1,646
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- ENNReal.ofNNRealproof · cited by 1,279
- ENNReal.ofRealproof · cited by 863
Cited by4
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.mutuallySingular_singularPartproof · cited by 6
- ProbabilityTheory.Kernel.withDensity_rnDeriv_mutuallySingularSetSliceproof · cited by 3
- MeasureTheory.Measure.MutuallySingular.compProd_of_rightproof · cited by 3
- ProbabilityTheory.Kernel.singularPart_of_subset_mutuallySingularSetSliceproof · cited by 1