Layerwise computability and image randomness
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 MartinLöf 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.
 Publication:

arXiv eprints
 Pub Date:
 July 2016
 arXiv:
 arXiv:1607.04232
 Bibcode:
 2016arXiv160704232B
 Keywords:

 Mathematics  Logic;
 Computer Science  Information Theory;
 Mathematics  Probability;
 03D32;
 G.3