Theorems · Theorem · sequences and series

Summable.nat_tsum_vanishing

∀ {G : Type u_2} [inst : AddCommGroup G] [inst_1 : TopologicalSpace G] [IsTopologicalAddGroup G] {f : ℕ → G},
  Summable f → ∀ ⦃e : Set G⦄, e ∈ nhds 0 → ∃ N, ∀ t ⊆ {n | N ≤ n}, ∑' (n : ↑t), f ↑n ∈ e

Defined in

Mathlib.Topology.Algebra.InfiniteSum.NatInt

Cited by

1 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupTopologicalSpaceIsTopologicalAddGroup