Theorems · Theorem · probability

ProbabilityTheory.aestronglyMeasurable_integral_condExpKernel

∀ {Ω : Type u_1} {F : Type u_2} {m : MeasurableSpace Ω} [mΩ : MeasurableSpace Ω] [inst : StandardBorelSpace Ω]
  {μ : MeasureTheory.Measure Ω} [inst_1 : MeasureTheory.IsFiniteMeasure μ] [inst_2 : NormedAddCommGroup F] {f : Ω → F}
  [inst_3 : NormedSpace ℝ F],
  MeasureTheory.AEStronglyMeasurable f μ →
    MeasureTheory.AEStronglyMeasurable (fun ω => ∫ (y : Ω), f y ∂(ProbabilityTheory.condExpKernel μ m) ω) μ

Defined in

Mathlib.Probability.Kernel.Condexp

Cited by

0 results in Mathlib

Foundations

Depth 285 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceStandardBorelSpaceMeasureTheory.IsFiniteMeasureNormedAddCommGroupNormedSpace