Theorems · Theorem · measure theory

Topology.IsEmbedding.aestronglyMeasurable_comp_iff

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : TopologicalSpace β] [inst_1 : TopologicalSpace γ]
  {m₀ : MeasurableSpace α} {μ : MeasureTheory.Measure α} [TopologicalSpace.PseudoMetrizableSpace β]
  [TopologicalSpace.PseudoMetrizableSpace γ] {g : β → γ} {f : α → β},
  Topology.IsEmbedding g →
    (MeasureTheory.AEStronglyMeasurable (fun x => g (f x)) μ ↔ MeasureTheory.AEStronglyMeasurable f μ)

Defined in

Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable

Cited by

6 results in Mathlib

Foundations

Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace.PseudoMetrizableSpaceTopologicalSpace.PseudoMetrizableSpace