The well-known characterization indicated in the title involves the moving maximal dyadic averages of the sequence (Xk: k = 1, 2, …) of random variables in Probability Theory. In the present paper, we offer another characterization of the SLLN
which does not require to form any maximum. Instead, it involves only a specially selected sequence of moving averages. The
results are also extended for random fields (Xkℓ: k, ℓ = 1, 2, …).