Effectively closed sets of measures and randomness
| dc.creator | Reimann, Jan | |
| dc.date | 2008-04-16 | |
| dc.date.accessioned | 2026-07-07T09:32:58Z | |
| dc.date.available | 2026-07-07T09:32:58Z | |
| dc.description | We show that if a real $x$ is strongly Hausdorff $h$-random, where $h$ is a dimension function corresponding to a convex order, then it is also random for a continuous probability measure $μ$ such that the $μ$-measure of the basic open cylinders shrinks according to $h$. The proof uses a new method to construct measures, based on effective (partial) continuous transformations and a basis theorem for $Π^0_1$-classes applied to closed sets of probability measures. We use the main result to give a new proof of Frostman's Lemma, to derive a collapse of randomness notions for Hausdorff measures, and to provide a characterization of effective Hausdorff dimension similar to Frostman's Theorem. | |
| dc.identifier | https://arxiv.org/abs/0804.2656 | |
| dc.identifier | http://arxiv.org/abs/0804.2656 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158974 | |
| dc.subject | Logic | |
| dc.subject | 03D80; 68Q30; 28C15 | |
| dc.title | Effectively closed sets of measures and randomness | |
| dc.type | text |