Strong Stability of Sums and Infinitely Divisible Distributions

The paper gives some new conditions for the strong law of large numbers (s. 1. 1. n.) to be applied to a sequence of independent symmetrical random variables (r. v.).
The principal result states that the s.1.1. n. for a sequence of “adjoined” infinitely divisible r. v. implies the s. 1. 1. n. for the given sequence of r. v.
This result leads to “satisfactory” sufficient conditions for s. l. l. n. In special cases some of these conditions become the necessary ones.