Theorems · Theorem · general topology

MeasurableSet.image_of_continuousOn_injOn

∀ {γ : Type u_3} {β : Type u_5} [inst : MeasurableSpace β] [tβ : TopologicalSpace β] [T2Space β] {s : Set γ} {f : γ → β}
  [OpensMeasurableSpace β] [tγ : TopologicalSpace γ] [PolishSpace γ] [inst_4 : MeasurableSpace γ] [BorelSpace γ],
  MeasurableSet s → ContinuousOn f s → Set.InjOn f s → MeasurableSet (f '' s)

The Lusin-Souslin theorem: if s is Borel-measurable in a Polish space, then its image under a continuous injective map is also Borel-measurable.

Defined in

Mathlib.MeasureTheory.Constructions.Polish.Basic

Cited by

6 results in Mathlib

Foundations

Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceT2SpaceOpensMeasurableSpaceTopologicalSpacePolishSpaceMeasurableSpaceBorelSpace