Theorems · Theorem · sequences and series
Summable.tendsto_atTop_zero
∀ {G : Type u_2} [inst : AddCommGroup G] [inst_1 : TopologicalSpace G] [IsTopologicalAddGroup G] {f : ℕ → G},
Summable f → Filter.Tendsto f Filter.atTop (nhds 0)- Cited by
- 10 results in Mathlib
- Foundations
- Depth 84 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.
- TopologicalSpacestatement and proof · cited by 24,529
- AddCommGroupstatement and proof · cited by 12,871
- Filterproof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement · cited by 2,405
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- Summablestatement and proof · cited by 778
- Nat.cofinite_eq_atTopproof · cited by 37
- Summable.tendsto_cofinite_zeroproof · cited by 16
Cited by10
Results whose statement or proof uses this declaration.
- summable_jacobiTheta₂_term_iffproof · cited by 4
- Summable.tsum_pow_mul_one_subproof · cited by 3
- Summable.one_sub_mul_tsum_powproof · cited by 3
- PeriodPair.hasFPowerSeriesOnBall_weierstrassPExceptproof · cited by 3
- FormalMultilinearSeries.le_radius_of_summable_normproof · cited by 3
- not_summable_of_ratio_norm_eventually_geproof · cited by 2
- hasFPowerSeriesAt_iffproof · cited by 1
- Summable.tendsto_atTop_of_posproof · cited by 1
- not_summable_of_antitone_of_negproof · cited by 1
- alternating_series_error_boundproof · cited by 0