Theorems · Theorem · general topology

ContinuousOn.measurableEmbedding

∀ {γ : Type u_3} {β : Type u_5} [inst : MeasurableSpace β] [tβ : TopologicalSpace β] [T2Space β] {s : Set γ} {f : γ → β}
  [BorelSpace β] [inst_3 : TopologicalSpace γ] [PolishSpace γ] [inst_5 : MeasurableSpace γ] [BorelSpace γ],
  MeasurableSet s → ContinuousOn f s → Set.InjOn f s → MeasurableEmbedding (s.domRestrict f)

If s is Borel-measurable in a Polish space and f is continuous injective on s, then the restriction of f to s is a measurable embedding.

Defined in

Mathlib.MeasureTheory.Constructions.Polish.Basic

Cited by

1 results in Mathlib

Foundations

Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceT2SpaceBorelSpaceTopologicalSpacePolishSpaceMeasurableSpaceBorelSpace