Theorems · Theorem · sequences and series

summable_iff_vanishing

∀ {α : Type u_1} {β : Type u_2} [inst : UniformSpace α] [inst_1 : AddCommGroup α] [IsUniformAddGroup α] {f : β → α}
  [CompleteSpace α], Summable f ↔ ∀ e ∈ nhds 0, ∃ s, ∀ (t : Finset β), Disjoint t s → ∑ b ∈ t, f b ∈ e

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Group

Cited by

1 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceAddCommGroupIsUniformAddGroupCompleteSpace