Theorems · Theorem · functional analysis

lp.hasSum_inner

∀ {ι : Type u_1} {𝕜 : Type u_2} [inst : RCLike 𝕜] {G : ι → Type u_4} [inst_1 : (i : ι) → NormedAddCommGroup (G i)]
  [inst_2 : (i : ι) → InnerProductSpace 𝕜 (G i)] (f g : ↥(lp G 2)),
  HasSum (fun i => inner 𝕜 (↑f i) (↑g i)) (inner 𝕜 f g)

Defined in

Mathlib.Analysis.InnerProductSpace.l2Space

Cited by

1 results in Mathlib

Foundations

Depth 231 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpace