Theorems · Theorem · sequences and series

Summable.tsum_finsetSum

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : AddCommMonoid α] [inst_1 : TopologicalSpace α]
  {L : SummationFilter β} [T2Space α] [ContinuousAdd α] [L.NeBot] {f : γ → β → α} {s : Finset γ},
  (∀ i ∈ s, Summable (f i) L) → ∑'[L] (b : β), ∑ i ∈ s, f i b = ∑ i ∈ s, ∑'[L] (b : β), f i b

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Basic

Cited by

5 results in Mathlib

Foundations

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

Assumes

AddCommMonoidTopologicalSpaceT2SpaceContinuousAddSummationFilter.NeBot