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On Skorokhod’s convergence. (English) Zbl 0969.60008

Korolyuk, V. (ed.) et al., Skorokhod’s ideas in probability theory. Kyïv: Institute of Mathematics of NAS of Ukraine. Proc. Inst. Math. Natl. Acad. Sci. Ukr., Math. Appl. 32, 53-60 (2000).
This paper was first published in [Teor. Veroyatn. Primen. 1, 239-247 (1956; Zbl 0074.34102)] in Russian. This is the translation of this paper. This paper contains a new definition of the Skorokhod’s convergence (\(S\)-convergence as it was defined in the paper) in a \(D\)-space of functions having only first order discontinuities which was introduced by A. V. Skorokhod [ibid. 1, 289-319 (1956; Zbl 0074.33802); for the English translation see below]. The new definition applies to a function \(f(t)\) of a real variable \(t\) which takes values in an arbitrary metric space. It is proved that the \(S\)-convergence may be generated by the metric \(s(f,g)\) which converts \(S\) into a complete metric space.
For the entire collection see [Zbl 0956.00022].

MSC:

60B10 Convergence of probability measures
60F17 Functional limit theorems; invariance principles
60G07 General theory of stochastic processes
60G05 Foundations of stochastic processes
60B11 Probability theory on linear topological spaces
01A75 Collected or selected works; reprintings or translations of classics
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