Theorems · Theorem · sequences and series
tsum_zero_pnat_eq_tsum_nat
∀ {G : Type u_2} [inst : AddCommGroup G] [inst_1 : TopologicalSpace G] [IsTopologicalAddGroup G] [T2Space G]
{f : ℕ → G}, Summable f → f 0 + ∑' (n : ℕ+), f ↑n = ∑' (n : ℕ), f n- Cited by
- 3 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- T2Spacestatement and proof · cited by 1,351
- tsumstatement and proof · cited by 1,148
- Summablestatement and proof · cited by 778
- PNatstatement and proof · cited by 392
- PNat.valstatement and proof · cited by 226
- add_right_injproof · cited by 71
- Summable.tsum_eq_zero_addproof · cited by 9
- tsum_pnat_eq_tsum_succproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- EisensteinSeries.qExpansion_identity_pnatproof · cited by 1
- tsum_int_eq_zero_add_tsum_pnatproof · cited by 1
- tendsto_zero_geometric_tsum_pnatproof · cited by 0