Theorems · Theorem · sequences and series

HasProdLocallyUniformlyOn.tendstoLocallyUniformlyOn_finsetRange

∀ {α : Type u_1} {β : Type u_2} [inst : CommMonoid α] {g : β → α} {s : Set β} [inst_1 : UniformSpace α]
  [inst_2 : TopologicalSpace β] {f : ℕ → β → α},
  HasProdLocallyUniformlyOn f g s → TendstoLocallyUniformlyOn (fun N b => ∏ i ∈ Finset.range N, f i b) g Filter.atTop s

Defined in

Mathlib.Topology.Algebra.InfiniteSum.UniformOn

Cited by

2 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidUniformSpaceTopologicalSpace