Probabilities of large deviations in the case of stable limit distributions (Q800023)

For independent random variables with common distribution function F from the domain of attraction of a stable law and with some special properties the equality \[ P(\sum^{n}_{j=1}X_ j\geq x)=nP(X_ 1\geq x)(1+o(1)) \] is valid uniformly with respect to x in some domain. This domain is described in terms of F. The result generalizes those of V. M. Zolotarev, L. V. Kim and A. V. Nagaev.