Theorems · Theorem · sequences and series

NNReal.summable_schlomilch_iff

∀ {C : ℕ} {u : ℕ → ℕ} {f : ℕ → NNReal},
  (∀ ⦃m n : ℕ⦄, 0 < m → m ≤ n → f n ≤ f m) →
    (∀ (n : ℕ), 0 < u n) →
      StrictMono u → C ≠ 0 → SuccDiffBounded C u → ((Summable fun k => (↑(u (k + 1)) - ↑(u k)) * f (u k)) ↔ Summable f)

for a series of NNReal version.

Defined in

Mathlib.Analysis.PSeries

Cited by

2 results in Mathlib

Foundations

Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound