Theorems · Definition · sequences and series

SummableUniformlyOn

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

SummableUniformlyOn f s means that there is some infinite sum to which f converges uniformly on s. Use fun x ↦ ∑' i, f i x to get the sum function.

Defined in

Mathlib.Topology.Algebra.InfiniteSum.UniformOn

Cited by

12 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidUniformSpace