Theorems · Theorem · sequences and series

summable_subtype_and_compl

∀ {α : Type u_1} {β : Type u_2} [inst : UniformSpace α] [inst_1 : AddCommGroup α] [IsUniformAddGroup α] {f : β → α}
  [CompleteSpace α] {s : Set β}, ((Summable fun x => f ↑x) ∧ Summable fun x => f ↑x) ↔ Summable f

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Group

Cited by

1 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceAddCommGroupIsUniformAddGroupCompleteSpace