Theorems · Theorem · sequences and series

Summable.sum_add_tsum_compl

∀ {α : Type u_1} {β : Type u_2} [inst : AddCommGroup α] [inst_1 : TopologicalSpace α] [IsTopologicalAddGroup α]
  {f : β → α} [T2Space α] {s : Finset β}, Summable f → ∑ x ∈ s, f x + ∑' (x : ↑(↑s)ᶜ), f ↑x = ∑' (x : β), f x

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Group

Cited by

1 results in Mathlib

Foundations

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

Assumes

AddCommGroupTopologicalSpaceIsTopologicalAddGroupT2Space