Theorems · Theorem · measure theory

stronglyMeasurable_iff_measurable_separable

∀ {α : Type u_1} {β : Type u_2} {f : α → β} {m : MeasurableSpace α} [inst : TopologicalSpace β]
  [TopologicalSpace.PseudoMetrizableSpace β] [inst_2 : MeasurableSpace β] [BorelSpace β],
  MeasureTheory.StronglyMeasurable f ↔ Measurable f ∧ TopologicalSpace.IsSeparable (Set.range f)

A function is strongly measurable if and only if it is measurable and has separable range.

Defined in

Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic

Cited by

13 results in Mathlib

Foundations

Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace.PseudoMetrizableSpaceMeasurableSpaceBorelSpace