Theorems · Theorem · measure theory

Topology.IsClosedEmbedding.continuousOn_comap_finiteMeasure

∀ {Ω : Type u_1} {Ω' : Type u_2} [inst : MeasurableSpace Ω] [inst_1 : MeasurableSpace Ω'] [inst_2 : TopologicalSpace Ω]
  [inst_3 : TopologicalSpace Ω'] [inst_4 : BorelSpace Ω] [inst_5 : BorelSpace Ω'] [NormalSpace Ω'] {f : Ω → Ω'},
  Topology.IsClosedEmbedding f →
    ContinuousOn (fun μ => MeasureTheory.FiniteMeasure.comap f μ) {μ | μ (Set.range f)ᶜ = 0}

Defined in

Mathlib.MeasureTheory.Measure.FiniteMeasure

Cited by

1 results in Mathlib

Foundations

Depth 256 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpaceTopologicalSpaceTopologicalSpaceBorelSpaceBorelSpaceNormalSpace