Theorems · Theorem · sequences and series

multipliableLocallyUniformlyOn_iff_hasProdLocallyUniformlyOn

∀ {α : Type u_1} {β : Type u_2} {ι : Type u_3} [inst : CommMonoid α] {f : ι → β → α} {s : Set β}
  [inst_1 : UniformSpace α] [inst_2 : TopologicalSpace β],
  MultipliableLocallyUniformlyOn f s ↔ HasProdLocallyUniformlyOn f (fun x => ∏' (i : ι), f i x) s

Defined in

Mathlib.Topology.Algebra.InfiniteSum.UniformOn

Cited by

0 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidUniformSpaceTopologicalSpace