The classic "Limit Dislribntions fOT slt1ns of Independent Ramdorn Vari- ables" by B. V. Gnedenko and A. N. Kolmogorov was published in 1949. Since then the theory of summation of independent variables has devel- oped rapidly. Today a summing-up of the studies in this area, and their results, would require many volumes. The monograph by I. A. Ibragi- mov and Yu. V. I~innik, "Independent and Stationarily Connected VaTiables", which appeared in 1965, contains an exposition of the contem- porary state of the theory of the summation of independent identically distributed random variables. The...