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Layerwise computability and image randomness (1607.04232v1)
Published 14 Jul 2016 in math.LO, cs.IT, math.IT, and math.PR
Abstract: Algorithmic randomness theory starts with a notion of an individual random object. To be reasonable, this notion should have some natural properties; in particular, an object should be random with respect to image distribution if and only if it has a random preimage. This result (for computable distributions and mappings, and Martin-L\"of randomness) was known for a long time (folklore); in this paper we prove its natural generalization for layerwise computable mappings, and discuss the related quantitative results.