Theorems · Theorem · sequences and series

ENNReal.le_tsum_schlomilch

∀ {u : ℕ → ℕ} {f : ℕ → ENNReal},
  (∀ ⦃m n : ℕ⦄, 0 < m → m ≤ n → f n ≤ f m) →
    (∀ (n : ℕ), 0 < u n) →
      StrictMono u → ∑' (k : ℕ), f k ≤ ∑ k ∈ Finset.range (u 0), f k + ∑' (k : ℕ), (↑(u (k + 1)) - ↑(u k)) * f (u k)

Defined in

Mathlib.Analysis.PSeries

Cited by

1 results in Mathlib

Foundations

Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound