7 citations · 17 across the 6 of their papers we have counts for
7 papers · 1 filter
Turing Degrees and Randomness for Continuous Measures
Mingyang Li, Jan Reimann
We study degree-theoretic properties of reals that are not random with respect to any continuous probability measure (NCR). To this end, we introduce a family of generalized Hausdo…
Effective Randomness for Continuous Measures
Jan Reimann, Theodore A. Slaman
We investigate which infinite binary sequences (reals) are effectively random with respect to some continuous (i.e., non-atomic) probability measure. We prove that for every n, all…
Finding subsets of positive measure
Bjørn Kjos-Hanssen, Jan Reimann
An important theorem of geometric measure theory (first proved by Besicovitch and Davies for Euclidean space) says that every analytic set of non-zero -dimensional Hausdorff mea…
Independence, Relative Randomness, and PA Degrees
Adam R. Day, Jan Reimann
We study pairs of reals that are mutually Martin-Löf random with respect to a common, not necessarily computable probability measure. We show that a generalized version of van Lamb…
Effectively closed sets of measures and randomness
Jan Reimann
We show that if a real is strongly Hausdorff -random, where is a dimension function corresponding to a convex order, then it is also random for a continuous probability…
Measures and their random reals
Jan Reimann, Theodore A. Slaman
We study the randomness properties of reals with respect to arbitrary probability measures on Cantor space. We show that every non-computable real is non-trivially random with resp…