Theorems · Theorem · measure theory

MeasureTheory.LocallyIntegrableOn.integrableOn_isCompact

∀ {X : Type u_1} {ε : Type u_3} [inst : MeasurableSpace X] [inst_1 : TopologicalSpace X] [inst_2 : TopologicalSpace ε]
  [inst_3 : ContinuousENorm ε] {f : X → ε} {μ : MeasureTheory.Measure X} {s : Set X}
  [TopologicalSpace.PseudoMetrizableSpace ε],
  MeasureTheory.LocallyIntegrableOn f s μ → IsCompact s → MeasureTheory.IntegrableOn f s μ

If a function is locally integrable on a compact set, then it is integrable on that set.

Defined in

Mathlib.MeasureTheory.Function.LocallyIntegrable

Cited by

2 results in Mathlib

Foundations

Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceTopologicalSpaceContinuousENormTopologicalSpace.PseudoMetrizableSpace