Theorems · Theorem · functional analysis
lp.summable_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)), Summable fun i => inner 𝕜 (↑f i) (↑g i)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 221 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- ENNRealstatement · cited by 9,879
- InnerProductSpacestatement and proof · cited by 3,523
- AddSubgroupstatement · cited by 3,232
- RCLikestatement and proof · cited by 2,829
- Nat.cast_oneproof · cited by 2,501
- SummationFilter.unconditionalstatement · cited by 2,068
- Inner.innerstatement · cited by 1,089
- Summablestatement · cited by 778
- PreLpstatement and proof · cited by 163
- lpstatement and proof · cited by 157
Cited by1
Results whose statement or proof uses this declaration.
- lp.hasSum_innerproof · cited by 1