Theorems · Theorem · probability

ProbabilityTheory.aestronglyMeasurable_trim_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}
  (hm : m ≤ mΩ) (hf : MeasureTheory.AEStronglyMeasurable f μ),
  ∀ᵐ (ω : Ω) ∂μ.trim hm, f =ᵐ[(ProbabilityTheory.condExpKernel μ m) ω] MeasureTheory.AEStronglyMeasurable.mk f hf

Defined in

Mathlib.Probability.Kernel.Condexp

Cited by

1 results in Mathlib

Foundations

Depth 287 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceStandardBorelSpaceMeasureTheory.IsFiniteMeasureNormedAddCommGroup