Layerwise computability and image randomness
  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. 
Laurent Bienvenu, Mathieu Hoyrup, Alexander Shen
math.LO cs.IT math.IT math.PR