Theorems · Theorem · measure theory

ContinuousLinearMap.integral_apply

∀ {X : Type u_1} {E : Type u_3} [inst : MeasurableSpace X] {μ : MeasureTheory.Measure X} {𝕜 : Type u_6}
  [inst_1 : RCLike 𝕜] [inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace 𝕜 E] [inst_4 : NormedSpace ℝ E]
  {H : Type u_8} [inst_5 : NormedAddCommGroup H] [inst_6 : NormedSpace 𝕜 H] {φ : X → H →L[𝕜] E},
  MeasureTheory.Integrable φ μ → ∀ (v : H), (∫ (x : X), φ x ∂μ) v = ∫ (x : X), (φ x) v ∂μ

Defined in

Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap

Cited by

5 results in Mathlib

Foundations

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

Assumes

MeasurableSpaceRCLikeNormedAddCommGroupNormedSpaceNormedSpaceNormedAddCommGroupNormedSpace