Theorems · Theorem · probability

ProbabilityTheory.Kernel.withDensity_one_sub_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 => ↑(1 - κ.rnDerivAux (κ + η) a x).toNNReal) = η

Defined in: Mathlib.Probability.Kernel.RadonNikodym
Cited by: 2 results in Mathlib
Foundations: Depth 328 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasurableSpace.CountableOrCountablyGenerated ProbabilityTheory.IsFiniteKernel ProbabilityTheory.IsFiniteKernel

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

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Cited by2

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ProbabilityTheory.Kernel.withDensity_rnDeriv_of_subset_compl_mutuallySingularSetSliceproof · cited by 1