Theorems · Theorem · probability
ProbabilityTheory.Kernel.measurable_singularPart_fun
∀ {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),
Measurable fun p =>
↑(κ.rnDerivAux (κ + η) p.1 p.2).toNNReal - ↑(1 - κ.rnDerivAux (κ + η) p.1 p.2).toNNReal * κ.rnDeriv η p.1 p.2- Defined in
- Mathlib.Probability.Kernel.RadonNikodym
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 215 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.
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- ENNRealstatement · cited by 9,879
- Measurablestatement · cited by 1,499
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- ENNReal.ofNNRealstatement · cited by 1,279
- Real.toNNRealstatement · cited by 267
- MeasurableSpace.CountableOrCountablyGeneratedstatement and proof · cited by 97
- ProbabilityTheory.Kernel.rnDerivstatement · cited by 45
- Measurable.fun_mulproof · cited by 30
- Measurable.coe_nnreal_ennrealproof · cited by 24
- ProbabilityTheory.Kernel.rnDerivAuxstatement · cited by 22
Cited by3
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.singularPart_compl_mutuallySingularSetSliceproof · cited by 4
- ProbabilityTheory.Kernel.measurable_singularPart_fun_rightproof · cited by 1
- ProbabilityTheory.Kernel.singularPart_of_subset_mutuallySingularSetSliceproof · cited by 1