Theorems · Theorem · probability
ProbabilityTheory.Kernel.withDensity_rnDeriv_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] [inst : ProbabilityTheory.IsFiniteKernel η] (a : α),
((η.withDensity (κ.rnDeriv η)) a) (κ.mutuallySingularSetSlice η a) = 0- Defined in
- Mathlib.Probability.Kernel.RadonNikodym
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 330 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- ProbabilityTheory.IsFiniteKernelstatement and proof · cited by 178
- MeasurableSpace.CountableOrCountablyGeneratedstatement and proof · cited by 97
- ProbabilityTheory.Kernel.rnDerivstatement and proof · cited by 45
- ProbabilityTheory.Kernel.withDensitystatement · cited by 45
- ProbabilityTheory.Kernel.mutuallySingularSetSlicestatement and proof · cited by 19
- ProbabilityTheory.Kernel.measurable_rnDerivproof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.withDensity_rnDeriv_eq_zero_iff_apply_eq_zeroproof · cited by 1
- ProbabilityTheory.Kernel.singularPart_eq_zero_iff_measure_eq_zeroproof · cited by 0