Theorems · Theorem · sequences and series

summable_schlomilch_iff_of_nonneg

∀ {C : ℕ} {u : ℕ → ℕ} {f : ℕ → ℝ},
  (∀ (n : ℕ), 0 ≤ f n) →
    (∀ ⦃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 series of nonnegative real numbers.

Defined in

Mathlib.Analysis.PSeries

Cited by

1 results in Mathlib

Foundations

Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound