Some properties of the range of super-Brownian motion.

Abstract. We consider a super-Brownian motion X. Its canonical measures can be studied through the path-valued process called the Brownian snake. We obtain the limiting behavior of the volume of the epsilon-neighborhood for the range of the Brownian snake, and as a consequence we derive the analogous result for the range of super-Brownian motion and for the support of the integrated super-Brownian excursion. Then we prove the support of X[sub t] is capacity-equivalent to [0, 1][sup 2] in R[sup d], d is greater than or equal to 3, and the range of X, as well as the support of the integrated super-Brownian excursion are capacity-equivalent to [0, 1][sup 4] in R[sup d] d less than or equal to 5. [ABSTRACT FROM AUTHOR]