Theorems · Theorem · measure theory

ContinuousOn.integrableOn_Icc

∀ {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} {a b : X}
  [MeasureTheory.IsFiniteMeasureOnCompacts μ] [inst_5 : Preorder X] [CompactIccSpace X] [T2Space X],
  ContinuousOn f (Set.Icc a b) → MeasureTheory.IntegrableOn f (Set.Icc a b) μ

Defined in

Mathlib.MeasureTheory.Function.LocallyIntegrable

Cited by

8 results in Mathlib

Foundations

Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceNormedAddCommGroupOpensMeasurableSpaceMeasureTheory.IsFiniteMeasureOnCompactsPreorderCompactIccSpaceT2Space