Theorems · Theorem · sequences and series

HasSumLocallyUniformlyOn.tsum_eqOn

∀ {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] [T2Space α],
  HasSumLocallyUniformlyOn f g s → Set.EqOn (fun x => ∑' (i : ι), f i x) g s

Defined in

Mathlib.Topology.Algebra.InfiniteSum.UniformOn

Cited by

2 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidUniformSpaceTopologicalSpaceT2Space