Theorems · Theorem · measure theory

ContinuousOn.integrableAt_nhdsWithin

∀ {α : Type u_1} {E : Type u_5} {mα : MeasurableSpace α} [inst : NormedAddCommGroup E] [inst_1 : TopologicalSpace α]
  [SecondCountableTopologyEither α E] [OpensMeasurableSpace α] {μ : MeasureTheory.Measure α}
  [MeasureTheory.IsLocallyFiniteMeasure μ] {a : α} {t : Set α} {f : α → E},
  ContinuousOn f t → MeasurableSet t → a ∈ t → MeasureTheory.IntegrableAtFilter f (nhdsWithin a t) μ

Defined in

Mathlib.MeasureTheory.Integral.IntegrableOn

Cited by

2 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupTopologicalSpaceSecondCountableTopologyEitherOpensMeasurableSpaceMeasureTheory.IsLocallyFiniteMeasure