arXiv 1607.042322016-07-14math.LOcs.ITmath.ITmath.PR

Layerwise computability and image randomness

Laurent Bienvenu, Mathieu Hoyrup, Alexander Shen

英文摘要：

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-Löf 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.

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