Theorems · Theorem · measure theory

MeasureTheory.setToFun_tsum

∀ {α : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
  [inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace ℝ F] {m : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  {T : Set α → E →L[ℝ] F} {C : ℝ} [CompleteSpace E] (hT : MeasureTheory.DominatedFinMeasAdditive μ T C) {ι : Type u_7}
  [Countable ι] {f : ι → α → E},
  (∀ (i : ι), MeasureTheory.AEStronglyMeasurable (f i) μ) →
    ∑' (i : ι), ∫⁻ (a : α), ‖f i a‖ₑ ∂μ ≠ ⊤ →
      (MeasureTheory.setToFun μ T hT fun a => ∑' (i : ι), f i a) = ∑' (i : ι), MeasureTheory.setToFun μ T hT (f i)

Defined in

Mathlib.MeasureTheory.Integral.SetToL1

Cited by

3 results in Mathlib

Foundations

Depth 246 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceCompleteSpaceCountable