Theorems · Theorem · measure theory

MeasureTheory.integral_add

∀ {α : Type u_1} {G : Type u_5} [inst : NormedAddCommGroup G] [inst_1 : NormedSpace ℝ G] {m : MeasurableSpace α}
  {μ : MeasureTheory.Measure α} {f g : α → G},
  MeasureTheory.Integrable f μ →
    MeasureTheory.Integrable g μ → ∫ (a : α), f a + g a ∂μ = ∫ (a : α), f a ∂μ + ∫ (a : α), g a ∂μ

Defined in

Mathlib.MeasureTheory.Integral.Bochner.Basic

Cited by

49 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupNormedSpace