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Teoriya Veroyatnostei i ee Primeneniya, 1998, Volume 43, Issue 4, Pages 781–786
DOI: https://doi.org/10.4213/tvp2079 (Mi tvp2079) 		 
Short Communications

On topological properties of the Skorokhod space

A. V. Kolesnikov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (1093 kB)
DOI: https://doi.org/10.4213/tvp2079
Abstract: We establish that, for a co-analytic set $X$ in a Polish space $E$, the Skorokhod space $D_1(X)$ is also co-analytic in the Polish space $D_1(E)$. At the same time, for a Suslin set $X \subset E$, $D_1(X)$ need not even be universally measurable in $D_1(E)$.
Keywords: Skorokhod space, Skorokhod topology, Polish space, Suslin (analytic) set, projective class, universally measurable set, space of closed subsets of a topological space.
Received: 25.11.1997
English version:
Theory of Probability and its Applications, 1999, Volume 43, Issue 4, Pages 640–644
DOI: https://doi.org/10.1137/S0040585X97977215
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. V. Kolesnikov, “On topological properties of the Skorokhod space”, Teor. Veroyatnost. i Primenen., 43:4 (1998), 781–786; Theory Probab. Appl., 43:4 (1999), 640–644
Citation in format AMSBIB
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\paper On topological properties of the Skorokhod space
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\pages 781--786
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\transl
\jour Theory Probab. Appl.
\yr 1999
\vol 43
\issue 4
\pages 640--644
\crossref{https://doi.org/10.1137/S0040585X97977215}
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  • https://www.mathnet.ru/eng/tvp/v43/i4/p781
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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