Theorems · Theorem · real analysis

curveIntegral_segment

∀ {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]
  [inst_6 : NormedSpace ℝ F] (ω : E → E →L[𝕜] F) (a b : E),
  ∫ᶜ (x : E) in Path.segment a b, ω x = ∫ (t : ℝ) in 0..1, (ω ((AffineMap.lineMap a b) t)) (b - a)

Defined in

Mathlib.MeasureTheory.Integral.CurveIntegral.Basic

Cited by

2 results in Mathlib

Foundations

Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedSpaceNormedSpace