ABSTRACT
The comparison of the classes of limit laws for “growing” random sums and for random sums of identically distributed summands in the double array scheme shows that in contrast to the classical summation theory the scheme of “growing” random sums is not a particular case of the double array scheme. The point is that the presence of a new source of randomness, namely, random indices, brings new in principle elements to the settings of the appearing problems. Within the consideration of random sums the centering of each summand inevitably leads to the situation where the sum itself will be centered by a random variable since the number of summands and consequently, of the constants centering each of them is random. The point is that the presence of a new source of randomness, namely, random indices, brings new in principle elements to the settings of the appearing problems.
