Theorems · Theorem · measure theory

MeasureTheory.integral_finsetSum_measure

∀ {α : Type u_1} {G : Type u_5} [inst : NormedAddCommGroup G] [inst_1 : NormedSpace ℝ G] {ι : Type u_6}
  {m : MeasurableSpace α} {f : α → G} {μ : ι → MeasureTheory.Measure α} {s : Finset ι},
  (∀ i ∈ s, MeasureTheory.Integrable f (μ i)) → ∫ (a : α), f a ∂∑ i ∈ s, μ i = ∑ i ∈ s, ∫ (a : α), f a ∂μ i

Defined in

Mathlib.MeasureTheory.Integral.Bochner.Basic

Cited by

4 results in Mathlib

Foundations

Depth 253 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace