Theorems · Theorem · sequences and series
SummationFilter.hasSum_symmetricIcc_iff
∀ {α : Type u_2} [inst : AddCommMonoid α] [inst_1 : TopologicalSpace α] {f : ℤ → α} {a : α},
HasSum f a (SummationFilter.symmetricIcc ℤ) ↔
Filter.Tendsto (fun N => ∑ n ∈ Finset.Icc (-↑N) ↑N, f n) Filter.atTop (nhds a)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites15
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
- Finsetproof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- nhdsstatement and proof · cited by 5,554
- Finset.sumstatement and proof · cited by 5,195
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- Filter.mapproof · cited by 819
- HasSumstatement · cited by 518
- Finset.Iccstatement and proof · cited by 348
- SummationFilter.filterproof · cited by 110
- Filter.map_mapproof · cited by 80
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