Theorems · Theorem · probability
ProbabilityTheory.Kernel.withDensity_rnDerivAux
∀ {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.IsFiniteKernel κ] [inst_1 : ProbabilityTheory.IsFiniteKernel η],
((κ + η).withDensity fun a x => ↑(κ.rnDerivAux (κ + η) a x).toNNReal) = κ- Defined in
- Mathlib.Probability.Kernel.RadonNikodym
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 327 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- ENNRealproof · cited by 9,879
- MeasurableSetproof · cited by 3,075
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- ENNReal.ofNNRealstatement · cited by 1,279
- MeasureTheory.Measure.extproof · cited by 308
- Real.toNNRealstatement · cited by 267
- ProbabilityTheory.IsFiniteKernelstatement and proof · cited by 178
- ProbabilityTheory.Kernel.extproof · cited by 116
- MeasurableSpace.CountableOrCountablyGeneratedstatement and proof · cited by 97
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.withDensity_one_sub_rnDerivAuxproof · cited by 2