Theorems · Theorem · measure theory

MeasureTheory.integral_add_measure

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

Defined in

Mathlib.MeasureTheory.Integral.Bochner.Basic

Cited by

9 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupNormedSpace