An a priori semimeasure (also known as “algorithmic probability” or “the Solomonoff prior” in the context of inductive inference) is defined as the transformation, by a given universal monotone Turing machine, of the uniform measure on the infinite strings. It is shown in this paper that the class of a priori semimeasures can equivalently be defined as the class of transformations, by all compatible universal monotone Turing machines, of any continuous computable measure in place of the uniform measure. Some consideration is given to possible implications for the association of algorithmic probability with certain foundational principles of statistics.

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Keywords A priori semimeasure, Algorithmic probability, Monotone turing machines, Occam’s razor, Principle of indifference, Semicomputable semimeasures
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Journal Theory of Computing Systems
Sterkenburg, T.F. (2017). A generalized characterization of algorithmic probability. Theory of Computing Systems, 61(4), 1337–1352. doi:10.1007/s00224-017-9774-9