Some topolocial properties of a random subset of Lebesgue measure zero

Abstract

The set of fast points associated with the process Y(s) = inf &ldet; x(t) &rdet; t&#8805 8 z ) where x(t) is a standard Brownian motion, is considered. This random subset of exceptional time set is shown to be everywhere dense of the second category and has the cardinality of the continuum. Journal of the Nigerian Association of Mathematical Physics Vol. 9 2005: pp. 57-60