Theorems · Theorem · measure theory

intervalIntegral.integral_smul_const

∀ {E : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {a b : ℝ} {μ : MeasureTheory.Measure ℝ}
  [CompleteSpace E] {𝕜 : Type u_8} [inst_3 : RCLike 𝕜] [inst_4 : NormedSpace 𝕜 E] (f : ℝ → 𝕜) (c : E),
  ∫ (x : ℝ) in a..b, f x • c ∂μ = (∫ (x : ℝ) in a..b, f x ∂μ) • c

Defined in

Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic

Cited by

2 results in Mathlib

Foundations

Depth 261 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceCompleteSpaceRCLikeNormedSpace