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Let W~{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 R>N,inf{dimF: F ∈ B(Rd), P{W(E) ∩ F ≠φ