Theorems · Theorem · real analysis

curveIntegral_segment_const

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] [inst_5 : NormedSpace ℝ E]
  [CompleteSpace F] (ω : E →L[𝕜] F) (a b : E), ∫ᶜ (x : E) in Path.segment a b, ω = ω (b - a)

Defined in

Mathlib.MeasureTheory.Integral.CurveIntegral.Basic

Cited by

1 results in Mathlib

Foundations

Depth 258 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedSpaceCompleteSpace