A subset of a topological space is said to be universally measurable if
it is measured by the completion of each countably additive finite Borel
measure on the space, and universally null if it has measure zero for
each such atomless measure. In 1908, Hausdorff proved that there exist
uncountable universally null sets, and thus that there exist at least
continuum many. Laver showed in the 1970's that consistently there are
just continuum many universally null sets. The question of whether there
exist more than continuum many universally measurable sets was asked by
Mauldin in 1978. We show that consistently there exist only continuum
many universally measurable sets. Many interesting questions about the
class of universally measurable sets remain open.