Ergodic theorems for random compact sets and fuzzy variables in Banach spaces (Q1182022)

First for compact set-valued random variables in \(L^ p\)-Banach spaces, an individual ergodic theorem is proved (w.r.t. Hausdorff-distances). By using the set representation of fuzzy sets, the appropriate ergodic theorems are proved for fuzzy set-valued random variables (w.r.t. three different types of convergence). The proofs generalize known methods of \textit{M. L. Puri} and \textit{D. A. Ralescu} [Ann. Probab. 11, 222--224 (1983; Zbl 0508.60021); J. Math. Anal. Appl. 91, 552--558 (1983; Zbl 0528.54009); ibid. 114, 409--422 (1986; Zbl 0592.60004); Math. Proc. Camb. Philos. Soc. 97, 151--158 (1985; Zbl 0559.60007)].