Theorems · Theorem · measure theory

MeasureTheory.StronglyMeasurable.of_countable_not_continuousAt

∀ {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},
  {x | ¬ContinuousAt f x}.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

0 results in Mathlib

Foundations

Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceOpensMeasurableSpaceMeasurableSingletonClassTopologicalSpaceTopologicalSpace.PseudoMetrizableSpaceSecondCountableTopologyEither