Theorems · Theorem · sequences and series

Pi.hasSum

∀ {α : Type u_1} {ι : Type u_4} {X : α → Type u_5} [inst : (x : α) → AddCommMonoid (X x)]
  [inst_1 : (x : α) → TopologicalSpace (X x)] {L : SummationFilter ι} {f : ι → (x : α) → X x} {g : (x : α) → X x},
  HasSum f g L ↔ ∀ (x : α), HasSum (fun i => f i x) (g x) L

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Constructions

Cited by

5 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidTopologicalSpace