Theorems · Theorem · measure theory

Measurable.stronglyMeasurable

∀ {α : Type u_1} {β : Type u_2} {f : α → β} {mα : MeasurableSpace α} [inst : MeasurableSpace β]
  [inst_1 : TopologicalSpace β] [TopologicalSpace.PseudoMetrizableSpace β] [SecondCountableTopology β]
  [OpensMeasurableSpace β], Measurable f → MeasureTheory.StronglyMeasurable f

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

Defined in

Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic

Cited by

47 results in Mathlib

Foundations

Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceTopologicalSpace.PseudoMetrizableSpaceSecondCountableTopologyOpensMeasurableSpace