  A uniform in probability approximation is established for Studentized
processes of non degenerate U-statistics of order m greater or equal to 2 in
terms of a standard Wiener process. The classical condition that the second
moment of kernel of the underlying U-statistic exists is relaxed to having 5/3
moments. Furthermore, the conditional expectation of the kernel is only assumed
to be in the domain of attraction of the normal law (instead of the classical
two moment condition).
