Theorems · Definition · measure theory

AEMeasurable

{α : Type u_1} →
  {β : Type u_2} →
    [MeasurableSpace β] →
      {_m : MeasurableSpace α} → (α → β) → autoParam (MeasureTheory.Measure α) AEMeasurable._auto_1 → Prop

A function is almost everywhere measurable if it coincides almost everywhere with a measurable function. A similar notion is MeasureTheory.NullMeasurable. That notion is equivalent to AEMeasurable if the σ-algebra on the codomain is countably generated, but weaker in general.

Defined in

Mathlib.MeasureTheory.Measure.MeasureSpaceDef

Cited by

840 results in Mathlib

Foundations

Depth 171 from the axioms, rests on 4,660 definitions · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace