Theorems · Theorem · sequences and series

HasProdLocallyUniformly.tendstoLocallyUniformly_finsetRange

∀ {α : Type u_1} {β : Type u_2} [inst : CommMonoid α] {g : β → α} [inst_1 : UniformSpace α]
  [inst_2 : TopologicalSpace β] {f : ℕ → β → α},
  HasProdLocallyUniformly f g → TendstoLocallyUniformly (fun x1 x2 => ∏ i ∈ Finset.range x1, f i x2) g Filter.atTop

Defined in

Mathlib.Topology.Algebra.InfiniteSum.UniformOn

Cited by

0 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidUniformSpaceTopologicalSpace