| In Radically Elementary Probability Theory Nelson applied nonstandard analysis to classical probability to prove many important theorems of probability. Although a sample space is finite in the approach Nelson uses, the finite number of objects in the sample space could be an unlimited natural number. Shafer generalizes probability in his monograph A Mathematical Theory of Evidence so that Bayesian probability is a special case in his theory of evidence. However, Shafer assumed that a frame of discernment (which is analogous to a sample space in classical probability) is finite in his monograph. But, such a finite number can be taken to be an unlimited natural number. Thus, much of Shafer's monograph extends to the case where the frame of discernment is an unlimited natural number. This dissertation explored additional results that can be obtained using nonstandard analysis. Several convergence results were obtained, and the Dempster-Shafer random variable was investigated. |
