  In this note we show that almost sure convergence to zero of symmetrized
U-statistics indexed by a linear sector in Z^d_+ is equivalent to convergence
along the diagonal of Z^d_+, as it is considered in Lata\la and Zinn [Ann.
Probab. 28 (2000) 1908-1924]. Comparisons with similar results for sums of
multi-indexed i.i.d. random variables are also made.
