Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.integral_tsum

∀ {ι : Type u_1} {X : Type u_2} {E : Type u_4} {F : Type u_5} {G : Type u_6} {mX : MeasurableSpace X}
  [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace ℝ F]
  [inst_4 : NormedAddCommGroup G] [inst_5 : NormedSpace ℝ G] {μ : MeasureTheory.VectorMeasure X F}
  {B : E →L[ℝ] F →L[ℝ] G} [CompleteSpace E] [Countable ι] {f : ι → X → E},
  (∀ (i : ι), MeasureTheory.AEStronglyMeasurable (f i) μ.variation) →
    ∑' (i : ι), ∫⁻ (a : X), ‖f i a‖ₑ ∂μ.variation ≠ ⊤ →
      ∫ᵛ (a : X), ∑' (i : ι), f i a ∂[B; μ] = ∑' (i : ι), ∫ᵛ (a : X), f i a ∂[B; μ]

Defined in

Mathlib.MeasureTheory.VectorMeasure.Integral

Cited by

1 results in Mathlib

Foundations

Depth 247 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceCompleteSpaceCountable