Theorems · Theorem · measure theory

aestronglyMeasurable_iUnion_iff

∀ {α : Type u_1} {β : Type u_2} {ι : Type u_4} [Countable ι] [inst : TopologicalSpace β] {m₀ : MeasurableSpace α}
  {μ : MeasureTheory.Measure α} {f : α → β} [TopologicalSpace.PseudoMetrizableSpace β] {s : ι → Set α},
  MeasureTheory.AEStronglyMeasurable f (μ.restrict (⋃ i, s i)) ↔
    ∀ (i : ι), MeasureTheory.AEStronglyMeasurable f (μ.restrict (s i))

Defined in

Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable

Cited by

2 results in Mathlib

Foundations

Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CountableTopologicalSpaceTopologicalSpace.PseudoMetrizableSpace