“…1, > Many authors generalized and extended this result without assumption of identical distribution in several directions. They studied the cases of independent, stochastically dominated random variables, triangular arrays of rowwise independent, stochastically dominated in the Cesaro sense random variables and sequences of independent random variables taking value in a Banach space ( Pruitt (1966), Rohatgi (1971), Hu, Moricz and Taylor (1989), Gut (1992), Wang, Bhaskara Rao 1 A c c e p t e d m a n u s c r i p t…”