Theorems · Theorem · measure theory

ContinuousOn.measurable_of_countable_compl

∀ {α : Type u_1} {γ : Type u_3} [inst : TopologicalSpace α] [inst_1 : MeasurableSpace α] [OpensMeasurableSpace α]
  [inst_3 : TopologicalSpace γ] [inst_4 : MeasurableSpace γ] [BorelSpace γ] [MeasurableSingletonClass α] {f : α → γ}
  {s : Set α}, ContinuousOn f s → sᶜ.Countable → Measurable f

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

Defined in

Mathlib.MeasureTheory.Constructions.BorelSpace.Basic

Cited by

1 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceMeasurableSpaceOpensMeasurableSpaceTopologicalSpaceMeasurableSpaceBorelSpaceMeasurableSingletonClass