Theorems · Theorem · measure theory

ContinuousOn.stronglyMeasurable_of_countable_compl

∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : TopologicalSpace α] [OpensMeasurableSpace α]
  [MeasurableSingletonClass α] [inst_4 : TopologicalSpace β] [TopologicalSpace.PseudoMetrizableSpace β]
  [h : SecondCountableTopologyEither α β] {f : α → β} {s : Set α},
  ContinuousOn f s → sᶜ.Countable → MeasureTheory.StronglyMeasurable f

If a function is continuous outside of a countable set, then it is strongly measurable.

Defined in

Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic

Cited by

1 results in Mathlib

Foundations

Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceOpensMeasurableSpaceMeasurableSingletonClassTopologicalSpaceTopologicalSpace.PseudoMetrizableSpaceSecondCountableTopologyEither