In mathematics, a subset A of a Polish space X is universally measurable if it is measurable with respect to every complete probability measure on X that measures all Borel subsets of X. In particular, a universally measurable set of reals is necessarily Lebesgue measurable (see #Finiteness condition) below.
Every analytic set is universally measurable. It follows from projective determinacy, which in turn follows from sufficient large cardinals, that every projective set is universally measurable.
Reference:
http://en.wikipedia.org/wiki/Universally_measurable_set
