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Measures on Boolean Algebras
Dissertation (MSc (Mathematics))--University of Pretoria, 2023.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2024
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| _version_ | 1867613468143648768 |
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| access_status_str | Open Access |
| author2 | Van der Walt, Jan Harm |
| author_browse | Van der Walt, Jan Harm |
| author_facet | Van der Walt, Jan Harm |
| collection | Thesis |
| dc_rights_str_mv | © 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. |
| description | Dissertation (MSc (Mathematics))--University of Pretoria, 2023. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/94470 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:36:37.472Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2024 |
| publishDateRange | 2024 |
| publishDateSort | 2024 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/94470 Measures on Boolean Algebras Van der Walt, Jan Harm u17049637@tuks.co.za Wortel, Marten Chamberlain, Tomas UCTD Measure Theory Boolean Algebras Dissertation (MSc (Mathematics))--University of Pretoria, 2023. 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. Mathematics and Applied Mathematics MSc (Mathematics) Unrestricted Faculty of Natural and Agricultural Sciences 2024-02-12T09:17:38Z 2024-02-12T09:17:38Z 2024-04 2023 Dissertation * A2024 http://hdl.handle.net/2263/94470 https://doi.org/10.25403/UPresearchdata.25196042 en © 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. application/pdf University of Pretoria |
| spellingShingle | UCTD Measure Theory Boolean Algebras Measures on Boolean Algebras |
| title | Measures on Boolean Algebras |
| title_full | Measures on Boolean Algebras |
| title_fullStr | Measures on Boolean Algebras |
| title_full_unstemmed | Measures on Boolean Algebras |
| title_short | Measures on Boolean Algebras |
| title_sort | measures on boolean algebras |
| topic | UCTD Measure Theory Boolean Algebras |
| url | http://hdl.handle.net/2263/94470 https://doi.org/10.25403/UPresearchdata.25196042 |