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Zbl 1020.60018
Lafuerza-Guillén, Bernardo; Sempi, Carlo
Probabilistic norms and convergence of random variables.
(English)
[J] J. Math. Anal. Appl. 280, No.1, 9-16 (2003). ISSN 0022-247X

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. {\it B. Schweizer} and {\it 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.
[Ulrich Stadtmüller (Ulm)]
MSC 2000:
*60F99 Limit theorems (probability)
28A20 Measurable and nonmeasurable functions
46S50 Functional analysis in probabilistic metric spaces
60B99 Probability theory on general structures

Keywords: convergence in probability; almost sure convergence; complete convergence; probabilistic normed space; probabilistic form

Citations: Zbl 0546.60010

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