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An extension of the Lindeberg–Feller theorem

V. I. Rotar'

Central Economics and Mathematics Institute, Academy of Sciences of the USSR

Abstract: A new version is presented of the necessary and sufficient condition of convergence, to a normal law, of sums of independent variables in a nonclassical situation (i.e., absence of limiting negligibility of variables). The obtained condition differs from previously obtained conditions by the fact that it does not use Levy's metric and that is is closer to classical formulations. A similar condition is sufficient for the closeness of two convolutions when the number of components of the convolutions increases without bounds.

UDC: 519.21.9

Received: 10.11.1974

 English version: Mathematical Notes, 1975, 18:1, 660–663

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