Theorems · Theorem · Lie groups

Summable.toCompl_tsum

∀ {α : Type u_1} {β : Type u_2} [inst : AddCommGroup α] [inst_1 : UniformSpace α] [inst_2 : IsUniformAddGroup α]
  {L : SummationFilter β} [L.NeBot] {f : β → α},
  Summable f L → ∑'[L] (i : β), UniformSpace.Completion.toCompl (f i) = ↑(∑'[L] (i : β), f i)

If a function f is summable in a uniform additive group α, then its sum in α is the same as its sum in Completion α.

Defined in

Mathlib.Topology.Algebra.InfiniteSum.GroupCompletion

Cited by

0 results in Mathlib

Foundations

Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupUniformSpaceIsUniformAddGroupSummationFilter.NeBot