  This paper investigates a new property of formal languages called
REG-measurability where REG is the class of regular languages. Intuitively, a
language \(L\) is REG-measurable if there exists an infinite sequence of
regular languages that "converges" to \(L\). A language without
REG-measurability has a complex shape in some sense so that it can not be
(asymptotically) approximated by regular languages. We show that several
context-free languages are REG-measurable (including languages with
transcendental generating function and transcendental density, in particular),
while a certain simple deterministic context-free language and the set of
primitive words are REG-immeasurable in a strong sense.
