Theorems · Theorem · measure theory

MeasurableEmbedding.integrableOn_map_iff

∀ {α : Type u_1} {β : Type u_2} {ε : Type u_3} {mα : MeasurableSpace α} [inst : TopologicalSpace ε]
  [inst_1 : ContinuousENorm ε] [inst_2 : MeasurableSpace β] {e : α → β},
  MeasurableEmbedding e →
    ∀ {f : β → ε} {μ : MeasureTheory.Measure α} {s : Set β},
      MeasureTheory.IntegrableOn f s (MeasureTheory.Measure.map e μ) ↔ MeasureTheory.IntegrableOn (f ∘ e) (e ⁻¹' s) μ

Defined in

Mathlib.MeasureTheory.Integral.IntegrableOn

Cited by

5 results in Mathlib

Foundations

Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceContinuousENormMeasurableSpace