lim — Mathlib

English

If n ↦ n • g(n) tends to t in a normed setting, then x ↦ x • g(⌊x⌋₊) tends to t as x → atTop.

Русский

Если n-смножение n • g(n) сходится к t, то x • g(⌊x⌋₊) сходится к t при x → atTop.

LaTeX

$$$\text{Tendsto}(n \mapsto n \cdot g(n))_{n\to\infty} = t \Rightarrow \text{Tendsto}(x \mapsto x \cdot g(\lfloor x \rfloor_+))_{x\to\infty} = t$$$

Lean4

/-- The limit of a bounded-below subadditive sequence. The fact that the sequence indeed tends to
this limit is given in `Subadditive.tendsto_lim` -/
@[nolint unusedArguments, irreducible]
protected def lim (_h : Subadditive u) :=
  sInf ((fun n : ℕ => u n / n) '' Ici 1)

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