Theorems · Theorem · approximation theory
summable_of_isBigO_nat
∀ {E : Type u_1} [inst : SeminormedAddCommGroup E] [CompleteSpace E] {f : ℕ → E} {g : ℕ → ℝ},
Summable g → f =O[Filter.atTop] g → Summable f- Defined in
- Mathlib.Analysis.Asymptotics.Lemmas
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- CompleteSpacestatement and proof · cited by 2,532
- Filter.atTopstatement and proof · cited by 2,405
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Summablestatement and proof · cited by 778
- Asymptotics.IsBigOstatement and proof · cited by 506
- Nat.cofinite_eq_atTopproof · cited by 37
- summable_of_isBigOproof · cited by 8
Cited by4
Results whose statement or proof uses this declaration.
- summable_pow_mul_jacobiTheta₂_term_boundproof · cited by 6
- summable_norm_mul_geometric_of_norm_lt_oneproof · cited by 2
- summable_norm_mul_geometric_of_norm_lt_one'proof · cited by 1
- summable_of_isBigO_nat'proof · cited by 1