Boolean-valued probabilistic metric spaces

In this paper the Boolean valued method is used to develop a theory closely resembling the theory of probabilistic metric spaces. In this development the complete Boolean algebra used must have the form of the quotient algebra of some atomless probability space ($\Omega,{\cal A},P$) modulo its class of null sets. In this setting the real numbers in the Boolean valued model, $V\sp{\cal B}$, correspond to random variables with domain $\Omega$, and the sets which act as binary operations on $\Re$ in the model correspond to binary operations on the class of random variables with domain $\Omega$.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Holsey, Mickey Charles

Contributors dc:contributor

• Takeuti, Gaisi

• Mathematics

Statement dc:rights

• Copyright 1989 Holsey, Mickey Charles

Language dc:language

eng

Identifier

AAI9010890
(UMI)AAI9010890

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/23263