Theorems · Theorem · probability

ProbabilityTheory.Kernel.eq_singularPart_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) → ξ a = (κ a).singularPart (η a)

Defined in: Mathlib.Probability.Kernel.RadonNikodym
Cited by: 2 results in Mathlib
Foundations: Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: ProbabilityTheory.IsFiniteKernel

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Cites17

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
add_commproof · cited by 1,535
Measurablestatement and proof · cited by 1,499
ProbabilityTheory.Kernelstatement and proof · cited by 1,281
MeasureTheory.Measure.withDensityproof · cited by 265
Measurable.compproof · cited by 234
ProbabilityTheory.IsFiniteKernelstatement and proof · cited by 178
add_applyproof · cited by 154
MeasureTheory.Measure.MutuallySingularstatement and proof · cited by 91

Cited by2

Results whose statement or proof uses this declaration.

ProbabilityTheory.Kernel.singularPart_eq_singularPart_measureproof · cited by 2
ProbabilityTheory.Kernel.eq_singularPartproof · cited by 0