Theorems · Theorem · probability

ProbabilityTheory.Kernel.withDensity_sub_add_cancel

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {κ : ProbabilityTheory.Kernel α β}
  [inst : ProbabilityTheory.IsSFiniteKernel κ] {f g : α → β → ENNReal},
  Measurable (Function.uncurry f) →
    Measurable (Function.uncurry g) →
      (∀ (a : α), g a ≤ᵐ[κ a] f a) → (κ.withDensity fun a x => f a x - g a x) + κ.withDensity g = κ.withDensity f

Defined in

Mathlib.Probability.Kernel.WithDensity

Cited by

1 results in Mathlib

Foundations

Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ProbabilityTheory.IsSFiniteKernel