Theorems · Theorem · real analysis

curveIntegral_trans

∀ {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},
  CurveIntegrable ω γab →
    CurveIntegrable ω γbc → ∫ᶜ (x : E) in γab.trans γbc, ω x = ∫ᶜ (x : E) in γab, ω x + ∫ᶜ (x : E) in γbc, ω x

Defined in

Mathlib.MeasureTheory.Integral.CurveIntegral.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

RCLikeNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace