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Superharmonic and multiply superharmonic functions and Jensen measures in axiomatic Brelot spaces

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.

Identiferoai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.115846
Date January 2009
CreatorsAlakhrass, Mohammad.
PublisherMcGill University
Source SetsLibrary and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada
LanguageEnglish
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation
Formatapplication/pdf
CoverageDoctor of Philosophy (Department of Mathematics and Statistics.)
RightsAll items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated.
Relationalephsysno: 003133127, proquestno: AAINR66596, Theses scanned by UMI/ProQuest.

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