布朗单的交差和逆象集的一致维数

The Variation and the Uniform Dimension of the Inverse Set of a Brownian Sheet

本文研究了布朗单的某些几何性质。设Ｗ（ｔ）：为布朗单，我们得到了布朗单变差的维数。当２Ｎ＞ｄ时，我们给出了布朗单在紧集上的逆象的一致Ｈｏｕｓｄｏｒｆｆ维数与一致Ｐａｃｋｉｎｇ维数的上Ｆ界。

In this paper,some geometric properties of browian sheets are investigated. Let W(t): Rd be a brownian sheet,we have obtained the dimension of the variation for the brownian sheet. When 2N>d,the uniform hausdorff dimension and upper bound and lower bound of the uniform packing dimension of inverse images of compact sets under W (t) are given.