Theorems · Theorem · sequences and series

hasSumLocallyUniformlyOn_iff_tendstoLocallyUniformlyOn

∀ {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] [inst_2 : TopologicalSpace β],
  HasSumLocallyUniformlyOn f g s ↔ TendstoLocallyUniformlyOn (fun x1 x2 => ∑ i ∈ x1, f i x2) g Filter.atTop s

Defined in

Mathlib.Topology.Algebra.InfiniteSum.UniformOn

Cited by

4 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidUniformSpaceTopologicalSpace