Theorems · Theorem · sequences and series
SummationFilter.hasProd_symmetricIco_int_iff
∀ {α : Type u_2} [inst : CommMonoid α] [inst_1 : TopologicalSpace α] {f : ℤ → α} {a : α},
HasProd f a (SummationFilter.symmetricIco ℤ) ↔
Filter.Tendsto (fun N => ∏ n ∈ Finset.Ico (-↑N) ↑N, f n) Filter.atTop (nhds a)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidTopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Filter.mapproof · cited by 819
- Finset.Icostatement and proof · cited by 450
- HasProdstatement · cited by 157
- SummationFilter.filterproof · cited by 110
- Filter.map_mapproof · cited by 80
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