Probabilistic norms and convergence of random variables
It is well-known that almost sure convergence is not metrizable. To circumvent this, the authors use the notion of probabilistic normed spaces, in particular Šerstnev spaces [see e.g. \textit{B. Schweizer} and \textit{A. Sklar}, ``Probabilistic metric spaces'' (1983; Zbl 0546.60010)] and construct a number of such spaces inducing different modes of convergence, as e.g., convergence in probability, \(L_p\)-convergence and almost sure convergence.
scientific article; zbMATH DE number 1915601
scientific article