Theorems · Theorem · measure theory

ContinuousOn.integrableOn_compact

∀ {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] {K : Set X} {f : X → E}
  [MeasureTheory.IsFiniteMeasureOnCompacts μ] [T2Space X],
  IsCompact K → ContinuousOn f K → MeasureTheory.IntegrableOn f K μ

Defined in

Mathlib.MeasureTheory.Function.LocallyIntegrable

Cited by

8 results in Mathlib

Foundations

Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceNormedAddCommGroupOpensMeasurableSpaceMeasureTheory.IsFiniteMeasureOnCompactsT2Space