Theorems · Theorem · functional analysis

HasSumUniformlyOn.of_norm_le_summable

∀ {α : Type u_1} {β : Type u_2} {F : Type u_3} [inst : NormedAddCommGroup F] [CompleteSpace F] {u : α → ℝ}
  {f : α → β → F},
  Summable u → ∀ {s : Set β}, (∀ (n : α), ∀ x ∈ s, ‖f n x‖ ≤ u n) → HasSumUniformlyOn f (fun x => ∑' (n : α), f n x) s

Defined in

Mathlib.Topology.Algebra.InfiniteSum.TsumUniformlyOn

Cited by

0 results in Mathlib

Foundations

Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupCompleteSpace