Theorems · Theorem · measure theory

MeasureTheory.MeasurePreserving.integrableOn_image

∀ {α : Type u_1} {β : Type u_2} {ε : Type u_3} {mα : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  [inst : TopologicalSpace ε] [inst_1 : ContinuousENorm ε] [inst_2 : MeasurableSpace β] {e : α → β}
  {ν : MeasureTheory.Measure β},
  MeasureTheory.MeasurePreserving e μ ν →
    MeasurableEmbedding e →
      ∀ {f : β → ε} {s : Set α}, MeasureTheory.IntegrableOn f (e '' s) ν ↔ MeasureTheory.IntegrableOn (f ∘ e) s μ

Defined in

Mathlib.MeasureTheory.Integral.IntegrableOn

Cited by

0 results in Mathlib

Foundations

Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceContinuousENormMeasurableSpace