  In this paper we give a positive answer to a question raised by Baer-Jerison
in connection with hyper-Jacobian determinants and associated minors in
fractional Sobolev spaces. Inspired by recent works of Brezis-Nguyen and
Baer-Jerison on the Jacobian and Hessian determinants, we show that the
distributional $m$th-Jacobian minors of degree $r$ are weak continuous in
fractional Sobolev spaces $W^{m-\frac{m}{r},r}$, and the result is optimal,
satisfying the necessary conditions, in the frame work of fractional Sobolev
spaces. In particular, the conditions can be removed in case $m=1,2$, i.e., the
$m$th-Jacobian minors of degree $r$ are well defined in $W^{s,p}$ if and only
if $W^{s,p} \subseteq W^{m-\frac{m}{r},m}$ in case $m=1,2$.
