Strong Law of Large Numbers for a Class of Dependent Random Variables

Let p >= 2. For a sequence of dependent p- integrable random variables, a sequence of positive real numbers {a(n),n >= 1} and a sequence of positive constants {b(n), >= 1}, conditions are provided under which the series Sigma(n)(i-1)(X-i - EXi)/h(i) converges almost surely as n ->infinity and {X-n, n >= 1} obeys the strong law of large numbers lim(n ->infinity)Sigma(n)(t=1) (X-i - EXi)/b(n) = 0 almost surely.