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Short Communications
On topological properties of the Skorokhod space
A. V. Kolesnikov M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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
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
Linking options:
https://www.mathnet.ru/eng/tvp2079https://doi.org/10.4213/tvp2079 https://www.mathnet.ru/eng/tvp/v43/i4/p781
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