Theorems · Theorem · measure theory

integral_smul_const

∀ {X : Type u_1} {E : Type u_3} [inst : MeasurableSpace X] {μ : MeasureTheory.Measure X} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace ℝ E] {𝕜 : Type u_8} [inst_3 : RCLike 𝕜] [inst_4 : NormedSpace 𝕜 E] [CompleteSpace E] (f : X → 𝕜)
  (c : E), ∫ (x : X), f x • c ∂μ = (∫ (x : X), f x ∂μ) • c

Defined in

Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap

Cited by

17 results in Mathlib

Foundations

Depth 260 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceNormedAddCommGroupNormedSpaceRCLikeNormedSpaceCompleteSpace