The collection of Borel sets (or analytic sets, etc.) in $\mathbb{R}$ has power $c = 2^{\aleph_0}$. But the collection of universally measurable sets has power $2^c$. This would follow from the existence of a universal null set of power $c$.
The collection of Borel sets (or analytic sets, etc.) has power $c = 2^{\aleph_0}$. But the collection of universally measurable sets has power $2^c$. This would follow from the existence of a universal null set of power $c$.