Theorems · Theorem · measure theory

AEMeasurable.aestronglyMeasurable

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

In a space with second countable topology, measurable implies strongly measurable.

Defined in

Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable

Cited by

57 results in Mathlib

Foundations

Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceMeasurableSpaceTopologicalSpace.PseudoMetrizableSpaceOpensMeasurableSpaceSecondCountableTopology