Theorems · Theorem · sequences and series

summable_condensed_iff_of_nonneg

∀ {f : ℕ → ℝ},
  (∀ (n : ℕ), 0 ≤ f n) → (∀ ⦃m n : ℕ⦄, 0 < m → m ≤ n → f n ≤ f m) → ((Summable fun k => 2 ^ k * f (2 ^ k)) ↔ Summable f)

Cauchy condensation test for antitone series of nonnegative real numbers.

Defined in

Mathlib.Analysis.PSeries

Cited by

2 results in Mathlib

Foundations

Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound