Theorems · Theorem · measure theory

Continuous.stronglyMeasurable

∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : TopologicalSpace α] [OpensMeasurableSpace α]
  [inst_3 : TopologicalSpace β] [TopologicalSpace.PseudoMetrizableSpace β] [h : SecondCountableTopologyEither α β]
  {f : α → β}, Continuous f → MeasureTheory.StronglyMeasurable f

A continuous function is strongly measurable when either the source space or the target space is second-countable.

Defined in

Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic

Cited by

7 results in Mathlib

Foundations

Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceOpensMeasurableSpaceTopologicalSpaceTopologicalSpace.PseudoMetrizableSpaceSecondCountableTopologyEither