English
The bounded limsup (blimsup) of a function along a filter, bounded by a predicate p, is the infimum of a such that for all x with p(x) the inequality u(x) ≤ a holds eventually.
Русский
Обобщенный предел верхний (blimsup) функции вдоль фильтра, ограниченный предикатом p, — инфимума всех a such that для всех x с p(x) справедливо u(x) ≤ a eventually.
LaTeX
$$$\operatorname{blimsup} (u,f,p) = \inf\{a : \forall^\infty x\in f,\ p(x) \to u(x) ≤ a\}$$$
Lean4
/-- The `blimsup` of a function `u` along a filter `f`, bounded by a predicate `p`, is the infimum
of the `a` such that the inequality `u x ≤ a` eventually holds for `f`, whenever `p x` holds. -/
def blimsup (u : β → α) (f : Filter β) (p : β → Prop) :=
sInf {a | ∀ᶠ x in f, p x → u x ≤ a}
