Discrete Stopping Times in Vector Lattices
Loading...
Date
Institution
http://id.loc.gov/authorities/names/n79058482
Degree Level
Master's
Degree
Master of Science
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematics
Supervisor / Co-Supervisor and Their Department(s)
Citation for Previous Publication
Link to Related Item
Abstract
The interplay between order structure and probability theory has long been studied. In recent years this has led a generalization of many of the concepts from probability theory to arbitrary vector lattices. In this thesis, we study the generalization of discrete stopping times in vector lattices. To do so, we first study the sup-completion of a vector lattice using the Maeda-Ogasawara representation of its universal completion. Using this, we show that the Daniell functional calculus for continuous functions is exactly the pointwise composition of functions in C(K), where K is the Stone space of the vector lattice. These tools allow us to study unbounded stopping times and obtain a ”nice” representation of them in vector lattices.
Item Type
http://purl.org/coar/resource_type/c_46ec
Alternative
License
Other License Text / Link
This thesis is made available by the University of Alberta Library with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
Subject/Keywords
Language
en