Journal
INFORMATION AND COMPUTATION
Volume 206, Issue 12, Pages 1375-1382Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.ic.2008.08.003
Keywords
Martin-Lof randomness; Conditional probability; Fubini's theorem; Relativized randomness; Kolmogorov complexity
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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. (C) 2008 Elsevier Inc. All rights reserved.
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