Another proof of a Sakhanenko theorem

We give an analytic proof of Sakhanenko's theorem on the strong law of large numbers. Our arguments are based on the method of characteristic functions: under the Lindeberg-type condition, the expectation of the absolute value of the sum of independent random variables (r.v.'s) tends to zero. In our proof, we represent the expectation of the absolute value of an r.v. in terms of the corresponding characteristic function.