Theorems · Theorem · functional analysis

HasSumUniformlyOn.of_norm_le_summable_eventually

∀ {β : Type u_2} {F : Type u_3} [inst : NormedAddCommGroup F] [CompleteSpace F] {ι : Type u_4} {f : ι → β → F}
  {u : ι → ℝ},
  Summable u →
    ∀ {s : Set β},
      (∀ᶠ (n : ι) in Filter.cofinite, ∀ x ∈ s, ‖f n x‖ ≤ u n) → HasSumUniformlyOn f (fun x => ∑' (n : ι), 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