Theorems · Theorem · functional analysis

tendstoUniformlyOn_tsum_nat_eventually

∀ {α : Type u_4} {F : Type u_5} [inst : NormedAddCommGroup F] [CompleteSpace F] {f : ℕ → α → F} {u : ℕ → ℝ},
  Summable u →
    ∀ {s : Set α},
      (∀ᶠ (n : ℕ) in Filter.atTop, ∀ x ∈ s, ‖f n x‖ ≤ u n) →
        TendstoUniformlyOn (fun N x => ∑ n ∈ Finset.range N, f n x) (fun x => ∑' (n : ℕ), f n x) Filter.atTop s

Defined in

Mathlib.Analysis.Normed.Group.FunctionSeries

Cited by

0 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupCompleteSpace