Theorems · Theorem · measure theory

MeasureTheory.integrableOn_iUnion_of_summable_integral_norm

∀ {X : Type u_1} {E : Type u_3} {mX : MeasurableSpace X} {ι : Type u_5} [Countable ι] {μ : MeasureTheory.Measure X}
  [inst : NormedAddCommGroup E] {f : X → E} {s : ι → Set X},
  (∀ (i : ι), MeasureTheory.IntegrableOn f (s i) μ) →
    (Summable fun i => ∫ (x : X) in s i, ‖f x‖ ∂μ) → MeasureTheory.IntegrableOn f (Set.iUnion s) μ

Defined in

Mathlib.MeasureTheory.Integral.Bochner.Set

Cited by

1 results in Mathlib

Foundations

Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CountableNormedAddCommGroup