Theorems · Theorem · approximation theory
Summable.mul_tendsto_const
∀ {F : Type u_1} {ι : Type u_2} [inst : NormedRing F] [NormMulClass F] [NormOneClass F] [CompleteSpace F] {f g : ι → F},
(Summable fun n => ‖f n‖) → ∀ {c : F}, Filter.Tendsto g Filter.cofinite (nhds c) → Summable fun n => f n * g n- Defined in
- Mathlib.Analysis.Asymptotics.Lemmas
- Cited by
- 1 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.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- nhdsstatement and proof · cited by 5,554
- Norm.normstatement and proof · cited by 5,413
- mul_oneproof · cited by 3,885
- Filter.Tendstostatement and proof · cited by 3,814
- one_mulproof · cited by 2,841
- CompleteSpacestatement and proof · cited by 2,532
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- NormedRingstatement and proof · cited by 924
- Summablestatement and proof · cited by 778
- Asymptotics.IsBigOproof · cited by 506
- Filter.cofinitestatement and proof · cited by 251
Cited by1
Results whose statement or proof uses this declaration.
- summable_norm_pow_mul_geometric_div_one_subproof · cited by 1