Trivial measures are not so trivial

Abstract

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.

Theory of Computing Systems, March 2015