Theorems · Theorem · measure theory

MeasureTheory.ae_eq_trim_iff_of_aestronglyMeasurable

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace β] [TopologicalSpace.MetrizableSpace β]
  {m m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f g : α → β} (hm : m ≤ m0)
  (hfm : MeasureTheory.AEStronglyMeasurable f μ) (hgm : MeasureTheory.AEStronglyMeasurable g μ),
  MeasureTheory.AEStronglyMeasurable.mk f hfm =ᵐ[μ.trim hm] MeasureTheory.AEStronglyMeasurable.mk g hgm ↔ f =ᵐ[μ] g

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable

Cited by

1 results in Mathlib

Foundations

Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace.MetrizableSpace