  We consider the possible sizes of large sumfree sets contained in the
discrete hypercube $\{1,...,n\}^k$, and we determine upper and lower bounds for
the maximal size as $n$ becomes large. We also discuss a continuous analogue in
which our lower bound remains valid and our upper bound can be strengthened,
and we consider the generalization of both problems to $l$-fold-sumfree sets.
