# Typicality of boundedness of entries of continued fraction representations

Is one of those claims about continued fractions true ?

$1)$ Almost all real numbers have a continued fraction representation with a bounded sequence of entries.

$2)$ Almost all real numbers have a continued fraction representation with an unbounded sequence of entries.

Intuitively I would expect that the unbounded sequence is the "typical" outcome. How can I determine the measure of both types of continued-fraction-sequences ?