Weak convergence of probability measures on the function space C([0, 1]2)

The existence of a Gaussian measure W on C([0, 1]2) with EW(x(s1,t1)·x(s2,t2))=min(s1,s2)·min(t1,t2) as its covariance function and an extension of Donsker's theorem for C([0, 1]2) are given.