@article{eprints989,
       publisher = {Elsevier},
         journal = {Expositiones mathematicae},
          author = {Irene Crimaldi},
          volume = {20},
          number = {4},
           pages = {375--384},
           title = {Convergence results for a normalized triangular array of symmetric random variables},
            year = {2002},
        abstract = {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.},
             url = {http://eprints.imtlucca.it/989/}
}