Trivial measures are not so trivial

Although algorithmic randomness with respect to various non-uniform computable measures is well-studied, little attention has been paid to algorithmic randomness with respect to computable \emph{trivial} measures, where a measure $\mu$ on $2^\omega$ is trivial if the support of $\mu$ consists of a countable collection of sequences. In this article, it is shown that there is much more structure to trivial computable measures than has been previously suspected.