Theorems · Theorem · measure theory

MeasureTheory.integral_tsum

∀ {α : Type u_1} {G : Type u_3} [inst : NormedAddCommGroup G] [inst_1 : NormedSpace ℝ G] {m : MeasurableSpace α}
  {μ : MeasureTheory.Measure α} {ι : Type u_4} [Countable ι] {f : ι → α → G},
  (∀ (i : ι), MeasureTheory.AEStronglyMeasurable (f i) μ) →
    ∑' (i : ι), ∫⁻ (a : α), ‖f i a‖ₑ ∂μ ≠ ⊤ → ∫ (a : α), ∑' (i : ι), f i a ∂μ = ∑' (i : ι), ∫ (a : α), f i a ∂μ

Defined in

Mathlib.MeasureTheory.Integral.DominatedConvergence

Cited by

3 results in Mathlib

Foundations

Depth 252 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceCountable