Theorems · Theorem · measure theory

measurable_indicator_const_iff

∀ {α : Type u_1} {β : Type u_2} {s : Set α} {m : MeasurableSpace α} {mβ : MeasurableSpace β} [inst : Zero β]
  [MeasurableSingletonClass β] (b : β) [NeZero b], Measurable (s.indicator fun x => b) ↔ MeasurableSet s

The measurability of a set A is equivalent to the measurability of the indicator function which takes a constant value b ≠ 0 on a set A and 0 elsewhere.

Defined in

Mathlib.MeasureTheory.MeasurableSpace.Basic

Cited by

4 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ZeroMeasurableSingletonClassNeZero