Theorems · Theorem · measure theory

MeasureTheory.integrableOn_finite_biUnion

∀ {α : Type u_1} {β : Type u_2} {ε : Type u_3} {mα : MeasurableSpace α} {f : α → ε} {μ : MeasureTheory.Measure α}
  [inst : TopologicalSpace ε] [inst_1 : ContinuousENorm ε] [TopologicalSpace.PseudoMetrizableSpace ε] {s : Set β},
  s.Finite →
    ∀ {t : β → Set α}, MeasureTheory.IntegrableOn f (⋃ i ∈ s, t i) μ ↔ ∀ i ∈ s, MeasureTheory.IntegrableOn f (t i) μ

Defined in

Mathlib.MeasureTheory.Integral.IntegrableOn

Cited by

1 results in Mathlib

Foundations

Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceContinuousENormTopologicalSpace.PseudoMetrizableSpace