  We show that, for $0<s<1$, $0<p<\infty$, $0<q<\infty$, Haj\l asz-Besov and
Haj\l asz-Triebel-Lizorkin functions can be approximated in the norm by
discrete median convolutions. This allows us to show that, for these functions,
the limit of medians, \[ \lim_{r\to 0}m_u^\gamma(B(x,r))=u^*(x), \] exists
quasieverywhere and defines a quasicontinuous representative of $u$. The above
limit exists quasieverywhere also for Haj\l asz functions $u\in M^{s,p}$,
$0<s\le 1$, $0<p<\infty$, but approximation of $u$ in $M^{s,p}$ by discrete
(median) convolutions is not in general possible.
