Vardy, Jessica Joy2013-07-252013-07-252013-07-25http://hdl.handle.net/10539/12905A dissertation submitted to the Faculty of Science, University of the Witwatersrand, in fulfillment of the requirements for the degree of Doctor of Philosophy, April 2013.In a series of papers by Wen-Chi Kuo, Coenraad Labuschagne and Bruce Watson results of martingale theory were generalised to the abstract setting of Riesz spaces. This thesis presents a survey of those results proved and aims to expand upon the work of these authors. In particular, independence results will be considered and these will be used to generalise well known results in the theory of Markov processes to Riesz spaces. Mixingales and quasi-martingales will be translated to the Riesz space setting.enRiesz spaces.Markov processes.Martingales (Mathematics)Thesis