A generalized characterization of algorithmic probability

A universal a priori semimeasure (also known as "algorithmic probability") is defined as the transformation, by a given universal monotone Turing machine, of the uniform measure on the infinite strings. We show in this paper that the class of universal a priori semimeasures can equivalently be defined as the class of transformations, by all compatible universal monotone Turing machines, of any nonatomic computable measure in place of the uniform measure.