Theorems · Theorem · sequences and series

Summable.sum_add_tsum_subtype_compl

∀ {α : Type u_1} {β : Type u_2} [inst : UniformSpace α] [inst_1 : AddCommGroup α] [IsUniformAddGroup α]
  [CompleteSpace α] [T2Space α] {f : β → α},
  Summable f → ∀ (s : Finset β), ∑ x ∈ s, f x + ∑' (x : { x // x ∉ s }), f ↑x = ∑' (x : β), f x

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Group

Cited by

3 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpaceAddCommGroupIsUniformAddGroupCompleteSpaceT2Space