Theorems · Theorem · measure theory

ContinuousOn.aestronglyMeasurable_of_subset_isCompact

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} [inst : TopologicalSpace α] [OpensMeasurableSpace α]
  [inst_2 : TopologicalSpace β] [TopologicalSpace.PseudoMetrizableSpace β] {f : α → β} {s t : Set α}
  {μ : MeasureTheory.Measure α},
  ContinuousOn f s → IsCompact s → MeasurableSet t → t ⊆ s → MeasureTheory.AEStronglyMeasurable f (μ.restrict t)

A function which is continuous on a compact set s is almost everywhere strongly measurable with respect to μ.restrict t for any measurable subset t of s.

Defined in

Mathlib.MeasureTheory.Integral.IntegrableOn

Cited by

2 results in Mathlib

Foundations

Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceOpensMeasurableSpaceTopologicalSpaceTopologicalSpace.PseudoMetrizableSpace