  It is well known that an $N$-parameter $d$-dimensional Brownian sheet has no
$k$-multiple points when $(k-1)d>2kN$, and does have such points when
$(k-1)d<2kN$. We complete the study of the existence of $k$-multiple points by
showing that in the critical cases where $(k-1)d=2kN$, there are a.s. no
$k$-multiple points.
