Theorems · Definition · measure theory

MeasureTheory.SimpleFunc.restrict

{α : Type u_1} →
  {β : Type u_2} →
    [inst : MeasurableSpace α] → [Zero β] → MeasureTheory.SimpleFunc α β → Set α → MeasureTheory.SimpleFunc α β

Restrict a simple function f : α →ₛ β to a set s. If s is measurable, then f.restrict s a = if a ∈ s then f a else 0, otherwise f.restrict s = const α 0.

Defined in

Mathlib.MeasureTheory.Function.SimpleFunc

Cited by

25 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceZero