Theorems · Theorem · measure theory

ContinuousOn.aemeasurable

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} [inst : TopologicalSpace α] [OpensMeasurableSpace α]
  [inst_2 : MeasurableSpace β] [inst_3 : TopologicalSpace β] [BorelSpace β] {f : α → β} {s : Set α}
  {μ : MeasureTheory.Measure α}, ContinuousOn f s → MeasurableSet s → AEMeasurable f (μ.restrict s)

A function which is continuous on a set s is almost everywhere measurable with respect to μ.restrict s.

Defined in

Mathlib.MeasureTheory.Integral.IntegrableOn

Cited by

4 results in Mathlib

Foundations

Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceOpensMeasurableSpaceMeasurableSpaceTopologicalSpaceBorelSpace