Theorems · Theorem · functional analysis
summable_iff_vanishing_norm
∀ {ι : Type u_1} {E : Type u_3} [inst : SeminormedAddCommGroup E] [CompleteSpace E] {f : ι → E},
Summable f ↔ ∀ ε > 0, ∃ s, ∀ (t : Finset ι), Disjoint t s → ‖∑ i ∈ t, f i‖ < ε- Cited by
- 2 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Finsetstatement and proof · cited by 13,712
- Norm.normstatement and proof · cited by 5,413
- Finset.sumstatement and proof · cited by 5,195
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- CompleteSpacestatement and proof · cited by 2,532
- Disjointstatement and proof · cited by 2,201
- SummationFilter.unconditionalstatement · cited by 2,068
- Summablestatement · cited by 778
- summable_iff_cauchySeq_finsetproof · cited by 9
- cauchySeq_finset_iff_vanishing_normproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- cauchySeq_finset_of_norm_bounded_eventuallyproof · cited by 2
- UnconditionalSchauderBasis.exists_norm_proj_leproof · cited by 1