Theorems · Theorem · probability

ProbabilityTheory.Kernel.setLIntegral_rnDeriv_le

∀ {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}
  [ProbabilityTheory.IsFiniteKernel κ] [ProbabilityTheory.IsFiniteKernel η] {a : α} {s : Set γ},
  MeasurableSet s → ∫⁻ (c : γ) in s, κ.rnDeriv η a c ∂η a ≤ (κ a) s

Defined in

Mathlib.Probability.Kernel.RadonNikodym

Cited by

1 results in Mathlib

Foundations

Depth 334 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace.CountableOrCountablyGeneratedProbabilityTheory.IsFiniteKernelProbabilityTheory.IsFiniteKernel