Theorems · Theorem · measure theory

MeasureTheory.condExp_tsum

∀ {α : Type u_1} {E : Type u_3} {m m₀ : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup E]
  [inst_1 : NormedSpace ℝ E] [CompleteSpace E] {ι : Type u_5} [Countable ι] {f : ι → α → E},
  (∀ (i : ι), MeasureTheory.AEStronglyMeasurable (f i) μ) →
    ∑' (i : ι), ∫⁻ (a : α), ‖f i a‖ₑ ∂μ ≠ ⊤ → μ[fun a => ∑' (i : ι), f i a | m] =ᵐ[μ] fun a => ∑' (i : ι), μ[f i | m] a

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic

Cited by

1 results in Mathlib

Foundations

Depth 297 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceCompleteSpaceCountable