Theorems · Theorem · sequences and series

hasSum_sum_support_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 ∈ L.support, b ∉ s → f b = 0) →
    ∀ [L.HasSupport] [inst_3 : DecidablePred fun x => x ∈ L.support], HasSum f (∑ b ∈ (↑s ∩ L.support).toFinset, 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

2 results in Mathlib

Foundations

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

Assumes

AddCommMonoidTopologicalSpaceSummationFilter.HasSupportDecidablePred