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'n Studie van die konveksiteitstelling van A.A. Lyapunov
Thesis (MSc (Mathematics))--University of Stellenbosch, 2008.
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| Format: | Thesis |
| Language: | Afrikaans |
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Stellenbosch : University of Stellenbosch
2008
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| _version_ | 1867614022997639168 |
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| access_status_str | Open Access |
| author | Barnard, Charlotte |
| author2 | Maritz, P. |
| author_browse | Barnard, Charlotte Maritz, P. |
| author_facet | Maritz, P. Barnard, Charlotte |
| author_sort | Barnard, Charlotte |
| collection | Thesis |
| dc_rights_str_mv | University of Stellenbosch |
| description | Thesis (MSc (Mathematics))--University of Stellenbosch, 2008. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/3106 |
| institution | Stellenbosch University (South Africa) |
| language | Afrikaans |
| last_indexed | 2026-06-10T12:45:26.037Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2008 |
| publishDateRange | 2008 |
| publishDateSort | 2008 |
| publisher | Stellenbosch : University of Stellenbosch |
| publisherStr | Stellenbosch : University of Stellenbosch |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/3106 'n Studie van die konveksiteitstelling van A.A. Lyapunov Barnard, Charlotte Maritz, P. University of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences. Lyapunov Dissertations -- Mathematics Theses -- Mathematics Convex geometry Convexity theorem Convexity measurement Konveksietietstelling Begrensde maat Nie-atomiese maat Thesis (MSc (Mathematics))--University of Stellenbosch, 2008. Let T be a non-empty set, A a u-algebra of subsets of T and u : .A -+ Rn a bounded, countably additive measure. A set E E A is called an atom with respect to u if u(E)=/F 0 and, if F E A, FeE, then u(F) = u(E) or u(F) = 0; the measure u is atomic if there exists at least one atom (with respect to u) in A. If no such atom (with respect to u) exists in A, then u is called non-atomic. In 1940 the Russian mathematician A. A. Lyapunov published the Convexity Theorem. According to this theorem the range 'R.{u) of a bounded, finite-dimensional measure u is compact and, in the non-atomic case, convex. Since 1940 much has been published on different aspects of the range of a vector-measure. These aspects range from new and shorter proofs of the Convexity Theorem and the usefulness of it in diverse fields, to research about the geometrical characteristics of the range by using other familiar theorems, like Krein-Milman and Radon-Nikodym. In the survey at hand the Convexity Theorem in itself is studied. Applications in different fields will be looked at as well as pieces about the history of the people and the ideas involved in the development of the theorem. 2008-09-11T08:06:04Z 2010-06-01T09:06:25Z 2008-09-11T08:06:04Z 2010-06-01T09:06:25Z 2008-03 Thesis http://hdl.handle.net/10019.1/3106 Afrikaans University of Stellenbosch application/pdf Stellenbosch : University of Stellenbosch |
| spellingShingle | Lyapunov Dissertations -- Mathematics Theses -- Mathematics Convex geometry Convexity theorem Convexity measurement Konveksietietstelling Begrensde maat Nie-atomiese maat Barnard, Charlotte 'n Studie van die konveksiteitstelling van A.A. Lyapunov |
| title | 'n Studie van die konveksiteitstelling van A.A. Lyapunov |
| title_full | 'n Studie van die konveksiteitstelling van A.A. Lyapunov |
| title_fullStr | 'n Studie van die konveksiteitstelling van A.A. Lyapunov |
| title_full_unstemmed | 'n Studie van die konveksiteitstelling van A.A. Lyapunov |
| title_short | 'n Studie van die konveksiteitstelling van A.A. Lyapunov |
| title_sort | n studie van die konveksiteitstelling van a a lyapunov |
| topic | Lyapunov Dissertations -- Mathematics Theses -- Mathematics Convex geometry Convexity theorem Convexity measurement Konveksietietstelling Begrensde maat Nie-atomiese maat |
| url | http://hdl.handle.net/10019.1/3106 |
| work_keys_str_mv | AT barnardcharlotte nstudievandiekonveksiteitstellingvanaalyapunov |