Summary
In this paper we try to argue that it is necessary to replace the topological convergence structure of Menger spaces with an appropriate probabilistic concept of convergence.
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References
Anthony, J. M., Sherwood, H. andTaylor, M.,Sequential convergence and probabilistic metric spaces. Rev. Roumaine Math. Pures Appl.19 (1974), 1177–1187.
Cech, E.,Topological spaces. Czechoslovak Academy of Sciences, Prague, 1966.
Drossos, C. A.,Stochastic Menger spaces and convergence in probability. Rev. Roumaine Math. Pures Appl.22 (1977), 1069–1076.
Florescu, L. C.,Structures syntopogènes probabilistes. Publ. Math. Debrecen28 (1981), 15–24.
Florescu, L. C.,Uniformities with a dilatation function. An. Ştiint. Univ. “Al. I. Cuza” Iaşi, Sect. I a Mat. (N.S.)27 (1981), 48–53.
Florescu, L. C.,Probabilistic pseudometrics. Mathematica (Cluj)24 (1982), 21–29.
Florescu, L. C.,Convergence and completeness in probabilistic spaces (Romanian). Proc. Nat. Conf. on Geometry and Topology, P. Neamt, June 1983. Univ. Al. I. Cuza, Iaşi, 1984, pp. 243–247.
Frank, M. J.,Probabilistic topological spaces. J. Math. Anal. Appl.34 (1971), 67–81.
Menger, K.,Statistical metrics. Proc. Nat. Acad. Sci. U.S.A.28 (1942), 535–537.
Mushtari, L. D. Kh.,On the completion of random metric spaces. Kazan. Gos. Univ. Učen. Zap.127 (1967), 109–119.
Schweizer, B. andSklar, A.,Statistical metric spaces. Pacific J. Math.10 (1960), 313–334.
Schweizer, B., Sklar, A. andThorp, E.,The metrization of statistical metric spaces. Pacific J. Math.10 (1960), 673–675.
Sherwood, H.,On the completion of probabilistic metric spaces. Z. Wahrsch. verw. Geb.6 (1966), 62–64.
Sherwood, H.,On E-spaces and their relation to other classes of probabilistic metric spaces. J. London Math. Soc.44 (1969), 441–448.
Tardiff, R. M.,Topologies for probabilistic metric spaces. Pacific J. Math.65 (1976), 233–251.
Thorp, E.,A Generalized topologies for statistical metric spaces. Fund. Math.51 (1962), 9–21.
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Florescu, L.C. Probabilistic convergence structures. Aeq. Math. 38, 123–145 (1989). https://doi.org/10.1007/BF01839999
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DOI: https://doi.org/10.1007/BF01839999