Theorems · Theorem · sequences and series

HasSumUniformlyOn.tendstoUniformlyOn

∀ {α : Type u_1} {β : Type u_2} {ι : Type u_3} [inst : AddCommMonoid α] {f : ι → β → α} {g : β → α} {s : Set β}
  [inst_1 : UniformSpace α],
  HasSumUniformlyOn f g s → TendstoUniformlyOn (fun x1 x2 => ∑ i ∈ x1, f i x2) g Filter.atTop s

Alias of the forward direction of hasSumUniformlyOn_iff_tendstoUniformlyOn.

Defined in

Mathlib.Topology.Algebra.InfiniteSum.UniformOn

Cited by

6 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidUniformSpace