Please be advised that the site will be down for maintenance on Sunday, September 1, 2024, from 08:00 to 18:00, and again on Monday, September 2, 2024, from 08:00 to 09:00. We apologize for any inconvenience this may cause.
dc.contributor.advisor | Van der Walt, Jan Harm | |
dc.contributor.coadvisor | Wortel, Marten | |
dc.contributor.postgraduate | Chamberlain, Tomas | |
dc.date.accessioned | 2024-02-12T09:17:38Z | |
dc.date.available | 2024-02-12T09:17:38Z | |
dc.date.created | 2024-04 | |
dc.date.issued | 2023 | |
dc.description | Dissertation (MSc (Mathematics))--University of Pretoria, 2023. | en_US |
dc.description.abstract | This thesis deals with a number of related results on Boolean algebras. First, we prove the Stone Representation Theorem, which shows that every Boolean algebra is isomorphic to an algebra of sets, namely the clopen algebra of its Stone space. Then we prove the Loomis-Sikorski Theorem, which shows exactly how the Stone Representation Theorem may be extended to represent countable suprema and infima in terms of unions and intersections of sets. Finally, we discuss strictly positive measures. We provide a characterisation, in terms of intersection numbers and covering numbers, of those Boolean algebras which admit strictly positive measures, and we conclude by showing that a σ-complete Boolean algebra admits a strictly positive σ-additive measure if and only if it admits a strictly positive measure and it is weakly σ-distributive. | en_US |
dc.description.availability | Unrestricted | en_US |
dc.description.degree | MSc (Mathematics) | en_US |
dc.description.department | Mathematics and Applied Mathematics | en_US |
dc.description.faculty | Faculty of Natural and Agricultural Sciences | en_US |
dc.identifier.citation | * | en_US |
dc.identifier.doi | https://doi.org/10.25403/UPresearchdata.25196042 | en_US |
dc.identifier.other | A2024 | en_US |
dc.identifier.uri | http://hdl.handle.net/2263/94470 | |
dc.language.iso | en | en_US |
dc.publisher | University of Pretoria | |
dc.rights | © 2023 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. | |
dc.subject | UCTD | en_US |
dc.subject | Measure Theory | en_US |
dc.subject | Boolean Algebras | en_US |
dc.title | Measures on Boolean Algebras | en_US |
dc.type | Dissertation | en_US |