Theorems · Theorem · measure theory

MeasureTheory.average_pair

∀ {α : Type u_1} {E : Type u_2} {F : Type u_3} {m0 : MeasurableSpace α} [inst : NormedAddCommGroup E]
  [inst_1 : NormedSpace ℝ E] [inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace ℝ F] [CompleteSpace F]
  {μ : MeasureTheory.Measure α} [CompleteSpace E] {f : α → E} {g : α → F},
  MeasureTheory.Integrable f μ →
    MeasureTheory.Integrable g μ → ⨍ (x : α), (f x, g x) ∂μ = (⨍ (x : α), f x ∂μ, ⨍ (x : α), g x ∂μ)

Defined in

Mathlib.MeasureTheory.Integral.Average

Cited by

2 results in Mathlib

Foundations

Depth 265 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceCompleteSpaceCompleteSpace