An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Process complexity and effective random tests
Journal of Computer and System Sciences
Algorithmic randomness and monotone complexity on product space
Information and Computation
Computable Bayesian compression for uniformly discretizable statistical models
ALT'09 Proceedings of the 20th international conference on Algorithmic learning theory
Algorithmic randomness and monotone complexity on product space
Information and Computation
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
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We study a universal Martin-Lof test with respect to a computable probability on a product space. Then, we define random sequences with respect to a conditional probability by using a section of the set of random points of product space. We show that (1) our definition is consistent with Fubini's theorem, and (2) it is equivalent to the relative notion of randomness under a condition. This is an extension of Lambalgen's theorem (1987) to a correlated probability.