Convergence theorems for fuzzy random variables and fuzzy martingales (Q1303966)

The author extends some results by \textit{M. L. Puri} and \textit{D. A. Ralescu} [J. Math. Anal. Appl. 114, 409-422 (1986; Zbl 0592.60004) and ibid. 160, No. 1, 107-122 (1991; Zbl 0737.60005)]. For fuzzy random variables, especially for fuzzy conditional expectation, dominated convergence theorems are proved. Furthermore, convergence theorems of fuzzy martingales are presented and proved by use of the well known embedding of fuzzy random variables into a Banach space of (support) functions. Sufficient conditions of closability for fuzzy martingales are discussed.