limsup — Mathlib

English

The liminf of a composition is the liminf of the outer function applied to the inner function after pushing the filter through the inner function.

Русский

Нижний предел композиции равен нижнему пределу внешней функции после переноса фильтра через внутреннюю.

LaTeX

$$$\liminf (u \circ v) f = \liminf u (\/map\; v\; f)$$$

Lean4

/-- The `limsup` of a function `u` along a filter `f` is the infimum of the `a` such that
the inequality `u x ≤ a` eventually holds for `f`. -/
def limsup (u : β → α) (f : Filter β) : α :=
  limsSup (map u f)

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