Theorems · Theorem · sequences and series

Summable.hasSum_iff

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

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Defs

Cited by

11 results in Mathlib

Foundations

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

Assumes

AddCommMonoidTopologicalSpaceT2SpaceSummationFilter.NeBot