Theorems · Theorem · measure theory

MeasureTheory.integrableOn_iff_comap_subtypeVal

∀ {α : Type u_1} {ε : Type u_3} {mα : MeasurableSpace α} {f : α → ε} {s : Set α} {μ : MeasureTheory.Measure α}
  [inst : TopologicalSpace ε] [inst_1 : ContinuousENorm ε],
  MeasurableSet s →
    (MeasureTheory.IntegrableOn f s μ ↔
      MeasureTheory.Integrable (f ∘ Subtype.val) (MeasureTheory.Measure.comap Subtype.val μ))

Defined in

Mathlib.MeasureTheory.Integral.IntegrableOn

Cited by

1 results in Mathlib

Foundations

Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceContinuousENorm