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

DOI: 10.4213/tvp2079

 English version: Theory of Probability and its Applications, 1999, 43:4, 640–644

Bibliographic databases:

• 
• 
•