## Tohoku Mathematical Journal 2002 September SECOND SERIES VOL. 54, NO. 3

 Tohoku Math. J. 54 (2002), 443-449

Title ON THE EXCEPTIONALITY OF SOME SEMIPOLAR SETS OF TIME INHOMOGENEOUS MARKOV PROCESSES

Author Yoichi Oshima

(Received July 17, 2000, revised May 10, 2001)
Abstract. For a Markov process associated with a not necessarily symmetric regular Dirichlet form, if the form satisfies the sector condition, then any semipolar sets are exceptional. On the other hand, in the case of the space-time Markov process associated with a family of time dependent Dirichlet forms, there exist non-exceptional semipolar sets. The main purpose of this paper is to show that any semipolar set $B=J\times \Gamma$ of the direct product type of a subset $J$ of time and a subset $\Gamma$ of space is exceptional if $J$ has positive Lebesgue measure.

2000 Mathematics Subject Classification. Primary 60J45; Secondary 60G07, 31C25.