Let Wˆ={W(t);t∈RN+} be the d-dimensional N-parameter Brownian Sheet.
Sufficient conditions for a compact set F⊂Rd∖{0} to be a polar set for W are proved. It is also proved
that if 2N≤d, then for any compact set E⊂RN>,
inf{dimF:F∈B(Rd),P{W(E)∩F≠ϕ}>0}=d−2DimE,
and if 2N>d, then for any compact set F⊂Rd∖{0},
inf{dimE:E∈B(RN>),P{W(E)∩F≠ϕ}>0}=d2−DimF2,
where B(Rd) and B(RN>) denote the Borel
σ-algebra in Rd and RN> respectively, and
dim and Dim are Hausdorff dimension and Packing dimension
respectively.