Theorems · Theorem · measure theory

LinearIsometry.integral_comp_comm

∀ {X : Type u_1} {E : Type u_3} {F : Type u_4} [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 : NormedAddCommGroup F]
  [CompleteSpace F] [inst_6 : NormedSpace 𝕜 F] [inst_7 : NormedSpace ℝ F] [CompleteSpace E] [inst_9 : NormedSpace ℝ E]
  (L : E →ₗᵢ[𝕜] F) (φ : X → E), ∫ (x : X), L (φ x) ∂μ = L (∫ (x : X), φ x ∂μ)

Defined in

Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap

Cited by

4 results in Mathlib

Foundations

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

Assumes

MeasurableSpaceRCLikeNormedAddCommGroupNormedSpaceNormedAddCommGroupCompleteSpaceNormedSpaceNormedSpaceCompleteSpaceNormedSpace