Theorems · Theorem · real analysis

curveIntegralFun_trans_aeeq_left

∀ {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] {a b c : E} (ω : E → E →L[𝕜] F)
  (γab : Path a b) (γbc : Path b c),
  curveIntegralFun ω (γab.trans γbc) =ᵐ[MeasureTheory.volume.restrict (Set.uIoc 0 (1 / 2))] fun t =>
    2 • curveIntegralFun ω γab (2 * t)

Defined in

Mathlib.MeasureTheory.Integral.CurveIntegral.Basic

Cited by

2 results in Mathlib

Foundations

Depth 245 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace