Equivalent conditions of complete convergence for m -dimensional products of iid random variables and application to strong law of large numbers

Under very weak condition 0＜ r(t) ↑∞, t →∞, we obtain a series of equivalent conditions of complete convergence for maxima of m -dimensional products of iid random variables, which provide a useful tool for researching this class of questions. Some results on strong law of large numbers are given such that our results are much stronger than the corresponding result of Gadidov's.