Theorems · Theorem · measure theory

Measurable.aestronglyMeasurable

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

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

Defined in

Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable

Cited by

59 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceMeasurableSpaceTopologicalSpace.PseudoMetrizableSpaceSecondCountableTopologyOpensMeasurableSpace