Some Polar Sets for the Generalized Brownian Sheet

Let (t)(t∈R +N) be the d-dimensional N-parameter generalized Brownian sheet.We study the polar sets for(t).It is proved that for any a∈R~d,P{(t) =a ,for some t ∈R >N} = 1,if βd<2N 0,if αd>2N and the probability that (t) has k-multiple points is 1 or 0 according as whether 2kN ∨d (k-1)βor 2kN ∧d(k-1)α .These results contain and extend the results of the Brownian sheet,where Rgt;~N =(0,+∞)~N ,R~N =[0,+∞)~N,0∧α≤ 1and β≥ 1.