We address the problem of fair division, or cake cutting, with the goal of
finding truthful mechanisms. In the case of a general measure space ("cake")
and non-atomic, additive individual preference measures - or utilities - we
show that there exists a truthful "mechanism" which ensures that each of the k
players gets at least 1/k of the cake. This mechanism also minimizes risk for
truthful players. Furthermore, in the case where there exist at least two
different measures we present a different truthful mechanism which ensures that
each of the players gets more than 1/k of the cake.

We then turn our attention to partitions of indivisible goods with bounded
utilities and a large number of goods. Here we provide similar mechanisms, but
with slightly weaker guarantees. These guarantees converge to those obtained in
the non-atomic case as the number of goods goes to infinity.