Theorems · Theorem · general topology

MeasurableSet.analyticSet_image

∀ {X : Type u_3} {Y : Type u_4} [inst : MeasurableSpace X] [StandardBorelSpace X] [inst_2 : TopologicalSpace Y]
  [inst_3 : MeasurableSpace Y] [OpensMeasurableSpace Y] {f : X → Y} [SecondCountableTopology ↑(Set.range f)]
  {s : Set X}, MeasurableSet s → Measurable f → MeasureTheory.AnalyticSet (f '' s)

The image of a measurable set in a standard Borel space under a measurable map is an analytic set.

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

MeasurableSpaceStandardBorelSpaceTopologicalSpaceMeasurableSpaceOpensMeasurableSpaceSecondCountableTopology