Theorems · Theorem · measure theory

Continuous.stronglyMeasurable_of_mulSupport_subset_isCompact

∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : TopologicalSpace α] [OpensMeasurableSpace α]
  [inst_3 : TopologicalSpace β] [TopologicalSpace.PseudoMetrizableSpace β] [inst_5 : One β] {f : α → β},
  Continuous f → ∀ {k : Set α}, IsCompact k → Function.mulSupport f ⊆ k → MeasureTheory.StronglyMeasurable f

A continuous function whose support is contained in a compact set is strongly measurable.

Defined in

Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic

Cited by

1 results in Mathlib

Foundations

Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceOpensMeasurableSpaceTopologicalSpaceTopologicalSpace.PseudoMetrizableSpaceOne