Good measures on Cantor space

While there is, up to homeomorphism, only one Cantor space, i.e. one zero-dimensional, perfect, compact, nonempty metric space, there are many measures on Cantor space which are not topologically equivalent. The clopen values set for a full, nonatomic measure $\mu$ is the countable dense subset $\{ \mu(U) : U$ is clopen$\}$ of the unit interval. It is a topological invariant for the measure. For the class of good measures it is a complete invariant. A full, nonatomic measure $\mu$ is good if whenever $U, V$ are clopen sets with $\mu(U) < \mu(V)$, there exists $W$ a clopen subset of $V$ such that $\mu(W) = \mu(U)$. These measures have interesting dynamical properties. They are exactly the measures which arise from uniquely ergodic minimal systems on Cantor space. For some of them there is a unique generic measure-preserving homeomorphism. That is, within the Polish group of such homeomorphisms there is a dense, $G_{\delta}$ conjugacy class.