Stochastic phase spaces,fuzzy sets,and statistical metric spaces

This paper is devoted to the study of the notion of the phase-space representation of quantum theory in both the nonrelativisitic and the relativisitic cases. Then, as a derived concept, the stochastic phase space is introduced and its connections with fuzzy set theory and probabilistic topological (in particular, metric) spaces are discussed.Supported by NSERC Grant No. A5206.On leave of absence from the Theoretical Physics Institute, University of Gdask, 80-952 Gdask, Poland.