Theorems · Theorem · probability
ProbabilityTheory.Kernel.rnDeriv_def
∀ {α : Type u_3} {γ : Type u_4} {mα : MeasurableSpace α} {mγ : MeasurableSpace γ}
[hαγ : MeasurableSpace.CountableOrCountablyGenerated α γ] (κ η : ProbabilityTheory.Kernel α γ) (a : α) (x : γ),
κ.rnDeriv η a x = ENNReal.ofReal (κ.rnDerivAux (κ + η) a x) / ENNReal.ofReal (1 - κ.rnDerivAux (κ + η) a x)- Defined in
- Mathlib.Probability.Kernel.RadonNikodym
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 213 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- ENNReal.ofRealstatement and proof · cited by 863
- MeasurableSpace.CountableOrCountablyGeneratedstatement and proof · cited by 97
- ProbabilityTheory.Kernel.rnDerivstatement · cited by 45
- ProbabilityTheory.Kernel.rnDerivAuxstatement and proof · cited by 22
Cited by5
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.measurable_rnDerivproof · cited by 11
- ProbabilityTheory.Kernel.singularPart_compl_mutuallySingularSetSliceproof · cited by 4
- ProbabilityTheory.Kernel.rnDeriv_def'proof · cited by 1
- ProbabilityTheory.Kernel.rnDeriv_eq_top_iffproof · cited by 1