The local times and Hausdorff measure for level sets of a Wiener sheet

In this paper, we discuss the relation between the local times and the level sets of a Wiener sheet, and give moment estimates for the local times of a Wiener sheet. We show that the correct Hausdorff measure function for level sets of N-parameter Rd-valued Wiener sheet is (r)=rN-d/2(loglog1/r)d/2 if 2N＞d. This solves the problem posed by S. J. Taylor.