Liouville Numbers, Borel Normality and Algorithmic Randomness

Calude,CS; Staiger, L

dc.contributor.author	Calude,CS	en
dc.contributor.author	Staiger, L	en
dc.date.accessioned	2014-01-05T22:48:17Z	en
dc.date.available	2014-01-05T22:48:17Z	en
dc.date.issued	2013	en
dc.identifier.citation	CDMTCS Research Reports CDMTCS-448 (2013)	en
dc.identifier.issn	1178-3540	en
dc.identifier.uri	http://hdl.handle.net/2292/21347	en
dc.description.abstract	We present a systematic comparison between Liouville, computable, Borel normal and Martin-Lof random numbers. The nine non-empty combinations, all small in measure or category, are illustrated with concrete examples. The sets of Liouville numbers and Martin-Lof random numbers are disjoint, thus showing that the irrationality exponent is not a measure of randomness. Finally, we construct the first computable set of correlations appearing in every Martin-Lof random number, but not in all numbers.	en
dc.publisher	Department of Computer Science, The University of Auckland, New Zealand	en
dc.relation.ispartofseries	CDMTCS Research Report Series	en
dc.rights	Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher.	en
dc.rights.uri	https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm	en
dc.source.uri	http://www.cs.auckland.ac.nz/staff-cgi-bin/mjd/secondcgi.pl?serial	en
dc.title	Liouville Numbers, Borel Normality and Algorithmic Randomness	en
dc.type	Technical Report	en
dc.subject.marsden	Fields of Research::280000 Information, Computing and Communication Sciences	en
dc.rights.holder	The author(s)	en
dc.rights.accessrights	http://purl.org/eprint/accessRights/OpenAccess	en