Theorems · Theorem · probability

ProbabilityTheory.Kernel.eq_rnDeriv_measure

∀ {α : Type u_1} {γ : Type u_2} {mα : MeasurableSpace α} {mγ : MeasurableSpace γ} {κ η ξ : ProbabilityTheory.Kernel α γ}
  {f : α → γ → ENNReal} [inst : ProbabilityTheory.IsFiniteKernel η],
  κ = η.withDensity f + ξ →
    Measurable (Function.uncurry f) → ∀ (a : α), (ξ a).MutuallySingular (η a) → f a =ᵐ[η a] (κ a).rnDeriv (η a)

Defined in: Mathlib.Probability.Kernel.RadonNikodym
Cited by: 2 results in Mathlib
Foundations: Depth 213 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: ProbabilityTheory.IsFiniteKernel

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Cites20

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

DFunLike.coestatement and proof · cited by 62,936
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealstatement and proof · cited by 9,879
MeasureTheory.aestatement · cited by 2,352
Filter.EventuallyEqstatement · cited by 1,912
add_commproof · cited by 1,535
Measurablestatement and proof · cited by 1,499
ProbabilityTheory.Kernelstatement and proof · cited by 1,281
Measurable.aemeasurableproof · cited by 304
MeasureTheory.Measure.withDensityproof · cited by 265
Measurable.compproof · cited by 234

Cited by2

Results whose statement or proof uses this declaration.

ProbabilityTheory.Kernel.rnDeriv_eq_rnDeriv_measureproof · cited by 13
ProbabilityTheory.Kernel.eq_rnDerivproof · cited by 0