Theorems · Theorem · sequences and series

SummableLocallyUniformlyOn.hasSumLocallyUniformlyOn

∀ {α : Type u_1} {β : Type u_2} {ι : Type u_3} [inst : AddCommMonoid α] {f : ι → β → α} {s : Set β}
  [inst_1 : UniformSpace α] [inst_2 : TopologicalSpace β],
  SummableLocallyUniformlyOn f s → HasSumLocallyUniformlyOn f (fun x => ∑' (i : ι), f i x) s

Defined in

Mathlib.Topology.Algebra.InfiniteSum.UniformOn

Cited by

3 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidUniformSpaceTopologicalSpace