Theorems · Definition · sequences and series

HasSumLocallyUniformlyOn

{α : Type u_1} →
  {β : Type u_2} →
    {ι : Type u_3} → [AddCommMonoid α] → (ι → β → α) → (β → α) → Set β → [UniformSpace α] → [TopologicalSpace β] → Prop

HasSumLocallyUniformlyOn f g s means that the (potentially infinite) sum ∑' i, f i b for b : β converges locally uniformly on s to g b (in the sense of TendstoLocallyUniformlyOn).

Defined in

Mathlib.Topology.Algebra.InfiniteSum.UniformOn

Cited by

16 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidUniformSpaceTopologicalSpace