Theorems · Theorem · measure theory

ContinuousOn.aestronglyMeasurable_of_isSeparable

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

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

Defined in

Mathlib.MeasureTheory.Integral.IntegrableOn

Cited by

1 results in Mathlib

Foundations

Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace.PseudoMetrizableSpaceOpensMeasurableSpaceTopologicalSpaceTopologicalSpace.PseudoMetrizableSpace