Theorems · Theorem · functional analysis
cauchySeq_finset_of_norm_bounded_eventually
∀ {ι : Type u_1} {E : Type u_3} [inst : SeminormedAddCommGroup E] {f : ι → E} {g : ι → ℝ},
Summable g → (∀ᶠ (i : ι) in Filter.cofinite, ‖f i‖ ≤ g i) → CauchySeq fun s => ∑ i ∈ s, f i- Cited by
- 2 results in Mathlib
- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Set.ofPredproof · cited by 6,101
- Norm.normstatement and proof · cited by 5,413
- Finset.sumstatement and proof · cited by 5,195
- Filter.Eventuallystatement and proof · cited by 3,134
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Disjointproof · cited by 2,201
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Summablestatement and proof · cited by 778
- Set.Finite.toFinsetproof · cited by 351
- le_sup_leftproof · cited by 265
Cited by2
Results whose statement or proof uses this declaration.
- Summable.of_norm_bounded_eventuallyproof · cited by 13
- cauchySeq_finset_of_norm_boundedproof · cited by 6