isLittleO_one_iff — Mathlib

English

A constant-one Big-O equivalence for bounded growth.

Русский

Эквивалентность Big-O с константой 1 для ограниченного роста.

LaTeX

$$IsBigO l f 1 ↔ IsBoundedUnder (≤) l (|f|)$$

Lean4

@[simp]
theorem isLittleO_one_iff {f : α → E'''} : f =o[l] (fun _x => 1 : α → F) ↔ Tendsto f l (𝓝 0) := by
  simp only [isLittleO_iff, norm_one, mul_one, Metric.nhds_basis_closedBall.tendsto_right_iff, Metric.mem_closedBall,
    dist_zero_right]

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