Theorems · Theorem · measure theory

Continuous.integrable_of_hasCompactSupport

∀ {X : Type u_1} {E : Type u_6} [inst : MeasurableSpace X] [inst_1 : TopologicalSpace X] [inst_2 : NormedAddCommGroup E]
  {μ : MeasureTheory.Measure X} [OpensMeasurableSpace X] {f : X → E} [MeasureTheory.IsFiniteMeasureOnCompacts μ],
  Continuous f → HasCompactSupport f → MeasureTheory.Integrable f μ

A continuous function with compact support is integrable on the whole space.

Defined in

Mathlib.MeasureTheory.Function.LocallyIntegrable

Cited by

18 results in Mathlib

Foundations

Depth 216 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceNormedAddCommGroupOpensMeasurableSpaceMeasureTheory.IsFiniteMeasureOnCompacts