Polar sets and relative dimension for generalized Brownian sheet

Let (W) over tilde (=) over cap {(W) over tilde (t); t is an element of R-+(N)} be a d-dimensional N-Parameter generalized Brownian Sheet. Necessary and sufficient conditions for a compact set E x F to be a polar set for (t, (W) over tilde (t)) are proved. It is also proved that if 2N <= alpha d, then for any compact set E subset of R->(N), d - 2/alpha DimE <= inf{dimF : F is an element of B(R-d), P{(W) over tilde (E) boolean AND F not equal 0} > 0} <= d - 2/beta Dim E, and if 2N > alpha d, then for any compact set F subset of R-d \ {0}, alpha/2 (d - DimF) <= inf{dimE : E is an element of B(R->(N)), P{(W) over tilde (E) boolean AND F not equal 0} > 0} <= beta/2(d - Dim F), where B(R-d) and B(R->(N)) denote the Borel sigma-algebra in R-d and in R->(N) respectively, dim and Dim are Hausdorff dimension and Packing dimension respectively.