%0 Journal Article
%@ 0723-0869
%A Crimaldi, Irene
%D 2002
%F eprints:989
%I Elsevier
%J Expositiones mathematicae
%N 4
%P 375-384
%T Convergence results for a normalized triangular array of symmetric random variables
%U http://eprints.imtlucca.it/989/
%V 20
%X For a triangular array of symmetric random variables (without any integrability condition) we replace the classical assumption of row-wise independence by that of row-wise joint symmetry. Under this weaker assumption we prove some results concerning the convergence in distribution of a suitable sequence of randomly normalized sums to the standard normal distribution. Then we exhibit a class of row-wise independent triangular arrays for which the ordinary sums fail to converge in distribution, while our results enable us to affirm the convergence in distribution of the normalized sums.