Theorems · Theorem · measure theory

MeasureTheory.NullMeasurable.aemeasurable_of_aerange

∀ {α : Type u_2} {β : Type u_3} {m0 : MeasurableSpace α} [inst : MeasurableSpace β] {μ : MeasureTheory.Measure α}
  {f : α → β} {t : Set β} [MeasurableSpace.CountablyGenerated ↑t],
  MeasureTheory.NullMeasurable f μ → (∀ᵐ (x : α) ∂μ, f x ∈ t) → AEMeasurable f μ

Let f : α → β be a null measurable function such that a.e. all values of f belong to a set t such that the restriction of the σ-algebra in the codomain to t is countably generated, then f is a.e.-measurable.

Defined in

Mathlib.MeasureTheory.Measure.AEMeasurable

Cited by

1 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpace.CountablyGenerated