Theorems · Theorem · measure theory

aemeasurable_indicator_const_iff

∀ {α : Type u_2} {β : Type u_3} {m0 : MeasurableSpace α} [inst : MeasurableSpace β] {μ : MeasureTheory.Measure α}
  [inst_1 : Zero β] {s : Set α} [MeasurableSingletonClass β] (b : β) [NeZero b],
  AEMeasurable (s.indicator fun x => b) μ ↔ MeasureTheory.NullMeasurableSet s μ

A characterization of the a.e.-measurability of the indicator function which takes a constant value b on a set A and 0 elsewhere.

Defined in

Mathlib.MeasureTheory.Measure.AEMeasurable

Cited by

5 results in Mathlib

Foundations

Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceZeroMeasurableSingletonClassNeZero