Theorems · Theorem · sequences and series

hasSum_sum

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : AddCommMonoid α] [inst_1 : TopologicalSpace α]
  {L : SummationFilter β} [ContinuousAdd α] {f : γ → β → α} {a : γ → α} {s : Finset γ},
  (∀ i ∈ s, HasSum (f i) (a i) L) → HasSum (fun b => ∑ i ∈ s, f i b) (∑ i ∈ s, a i) L

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Basic

Cited by

4 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidTopologicalSpaceContinuousAdd