Theorems · Theorem · sequences and series
Summable.tsum_eq_zero_add
∀ {G : Type u_2} [inst : AddCommGroup G] [inst_1 : TopologicalSpace G] [IsTopologicalAddGroup G] [T2Space G]
{f : ℕ → G}, Summable f → ∑' (b : ℕ), f b = f 0 + ∑' (b : ℕ), f (b + 1)- Cited by
- 9 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 1,148
- Summablestatement and proof · cited by 778
- summable_nat_add_iffproof · cited by 24
- tsum_eq_zero_add'proof · cited by 3
Cited by9
Results whose statement or proof uses this declaration.
- zeta_eq_tsum_one_div_nat_add_one_cpowproof · cited by 3
- tsum_zero_pnat_eq_tsum_natproof · cited by 3
- tsum_riemannZetaSummandproof · cited by 2
- geom_series_succproof · cited by 2
- Cardinal.cantorFunction_succproof · cited by 1
- spectrum.exp_mem_expproof · cited by 1
- tsum_geometric_le_of_norm_lt_oneproof · cited by 1
- HurwitzKernelBounds.F_nat_zero_zero_sub_leproof · cited by 1
- tsum_eq_tsum_primes_add_tsum_primes_of_support_subset_prime_powersproof · cited by 0