Theorems · Theorem · sequences and series

hasSum_sum_of_ne_finset_zero

∀ {α : Type u_1} {β : Type u_2} [inst : AddCommMonoid α] [inst_1 : TopologicalSpace α] {L : SummationFilter β}
  {f : β → α} {s : Finset β}, (∀ b ∉ s, f b = 0) → ∀ [L.LeAtTop], HasSum f (∑ b ∈ s, f b) L

If a function f vanishes outside of a finite set s, then it HasSum ∑ b ∈ s, f b.

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Defs

Cited by

5 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidTopologicalSpaceSummationFilter.LeAtTop