We study quasi superharmonic functions in Brelot spaces and the relationship between a reduced function, and harmonic and Jensen measures. We introduce the concept of quasi multiply superharmonic functions on a product of two Brelot spaces and study their properties. A main result obtained is characterizing the quasi superharmonic functions in terms of harmonic, finely harmonic and Jensen measures. Then we prove that a quasi multiply superharmonic function on a product of Brelot spaces equals its lower semicontinuous regularization out side of a 2-negligible set. Further we give a sufficient condition on a Brelot space O under which O becomes an extension space for superharmonic functions. As a result we characterize the extreme Jensen measures in such spaces. Finally we study extreme Jensen measures relative to several classes of multiply superharmonic functions.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.115846 |
| Date | January 2009 |
| Creators | Alakhrass, Mohammad. |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Mathematics and Statistics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 003133127, proquestno: AAINR66596, Theses scanned by UMI/ProQuest. |
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