Theorems · Theorem · measure theory

intervalIntegral.integral_add

∀ {E : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {a b : ℝ} {f g : ℝ → E}
  {μ : MeasureTheory.Measure ℝ},
  IntervalIntegrable f μ a b →
    IntervalIntegrable g μ a b → ∫ (x : ℝ) in a..b, f x + g x ∂μ = ∫ (x : ℝ) in a..b, f x ∂μ + ∫ (x : ℝ) in a..b, g x ∂μ

Defined in

Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic

Cited by

7 results in Mathlib

Foundations

Depth 256 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace