Theorems · Theorem · measure theory

Continuous.isOpenPosMeasure_map

∀ {X : Type u_1} [inst : TopologicalSpace X] {m : MeasurableSpace X} {μ : MeasureTheory.Measure X} [μ.IsOpenPosMeasure]
  [OpensMeasurableSpace X] {Z : Type u_3} [inst_3 : TopologicalSpace Z] [inst_4 : MeasurableSpace Z] [BorelSpace Z]
  {f : X → Z}, Continuous f → Function.Surjective f → (MeasureTheory.Measure.map f μ).IsOpenPosMeasure

Defined in

Mathlib.MeasureTheory.Measure.OpenPos

Cited by

4 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceMeasureTheory.Measure.IsOpenPosMeasureOpensMeasurableSpaceTopologicalSpaceMeasurableSpaceBorelSpace