Bandits.UCB.constSum_lt_top🔗

This page has the declaration's own card below, then its dependency graph, then a card for each dependency (type dependencies first, then the rest of the transitive closure). For a theorem, the graph and the dependency cards only follow its statement's dependencies (its proof is replaced by sorry, so what it proves doesn't depend on how); for everything else, both the type and the body/value are followed, since their content is part of what later declarations build on.

Minimal Lean file

Bandits.UCB.constSum_lt_top (c : ℝ) (n : ℕ) : constSum c n < ⊤
Bandits.UCB.constSum_lt_top (c : ℝ)
  (n : ℕ) : constSum c n < ⊤

lemma constSum_lt_top (c : ℝ) (n : ℕ) : constSum c n < ∞

by
  rw [constSum, ENNReal.sum_lt_top]
  intro k hk
  simp only [one_div, ENNReal.inv_lt_top]
  positivity

Dependency graph

Type dependencies (1)

Bandits.UCB.constSum (c : ℝ) (n : ℕ) : ENNReal
Bandits.UCB.constSum (c : ℝ) (n : ℕ) :
  ENNReal

noncomputable
def constSum (c : ℝ) (n : ℕ) : ℝ≥0∞ := ∑ s ∈ range n, 1 / ((s : ℝ≥0∞) + 1) ^ (c - 1)