Introduction. The sums formed from the set of non-negative powers of 2 are just the non-negative integers. It is easy to obtain “abelian” results to the effect that if a set is distributed like the powers of 2, then the sum set will be distributed like Dhe non-negative integers. We will be concerned here with converse, or “Tauberian” results. The main theme of this paper is t’he following quest...

we then write sn → s(A), where A is the A method of summability. Appropriate choices of A= [an,k] for n,k ≥ 0 give the classical methods [2]. In this paper, we present various summability analogs of the strong law of large numbers (SLLN) and their rates of convergence in an unified setting, beyond the class of random-walk methods. A convolution summability method introduced in the next section ...