Theorems · Theorem · sequences and series

tsum_eq_of_summable_unconditional

∀ {α : Type u_1} {β : Type u_2} [inst : AddCommMonoid α] [inst_1 : TopologicalSpace α] {L : SummationFilter β}
  {f : β → α} [T2Space α] [L.NeBot] [L.LeAtTop], Summable f → ∑'[L] (b : β), f b = ∑' (b : β), f b

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Defs

Cited by

0 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidTopologicalSpaceT2SpaceSummationFilter.NeBotSummationFilter.LeAtTop