Convergence of series of independent random variables

Sufficient conditions are given for the convergence almost surely of a series composed of independent symmetric random variables.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Mateamticheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 158, pp. 158–160, 1987.