Theorems · Theorem · measure theory

Continuous.aestronglyMeasurable

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace β] {m₀ : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  {f : α → β} [inst_1 : TopologicalSpace α] [OpensMeasurableSpace α] [TopologicalSpace.PseudoMetrizableSpace β]
  [SecondCountableTopologyEither α β], Continuous f → MeasureTheory.AEStronglyMeasurable f μ

A continuous function from α to β is ae strongly measurable when one of the two spaces is second countable.

Defined in

Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable

Cited by

70 results in Mathlib

Foundations

Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceOpensMeasurableSpaceTopologicalSpace.PseudoMetrizableSpaceSecondCountableTopologyEither