  We study the Banach space $D([0,1]^m)$ of functions of several variables that
are (in a certain sense) right-continuous with left limits, and extend several
results previously known for the standard case $m=1$. We give, for example, a
description of the dual space, and we show that a bounded multilinear form
always is measurable with respect to the $\sigma$-field generated by the point
evaluations. These results are used to study random functions in the space.
(I.e., random elements of the space.) In particular, we give results on
existence of moments (in different senses) of such random functions, and we
give an application to the Zolotarev distance between two such random
functions.
