Bienvenu, L, Holzl, R, Porter, CP et al. (1 more author) (2017) Randomness and semimeasures. Notre Dame Journal of Formal Logic, 58 (3). pp. 301-328. ISSN 0029-4527
Abstract
A semimeasure is a generalization of a probability measure obtained by relaxing the additivity requirement to superadditivity. We introduce and study several randomness notions for left-c.e. semimeasures, a natural class of effectively approximable semimeasures induced by Turing functionals. Among the randomness notions we consider, the generalization of weak 2-randomness to left-c.e. semimeasures is the most compelling, as it best reflects Martin-Löf randomness with respect to a computable measure. Additionally, we analyze a question of Shen, a positive answer to which would also have yielded a reasonable randomness notion for left-c.e. semimeasures. Unfortunately, though, we find a negative answer, except for some special cases.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2017 by University of Notre Dame. This is an author produced version of a paper published in the Notre Dame Journal of Formal Logic. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | semimeasures; measures; algorithmic randomness; randomness |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 24 Feb 2017 12:21 |
Last Modified: | 19 Jan 2018 06:20 |
Status: | Published |
Publisher: | University of Notre Dame |
Identification Number: | 10.1215/00294527-3839446 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:111911 |