(Received December 5, 1989; revised May 23, 1990)
Abstract. Several characterizations of multivariate stable distributions together with a characterization of multivariate normal distributions and multivariate stable distributions with Cauchy marginals are given. These are related to some standard characterizations of Marcinkiewicz.
Key words and phrases: Multivariate stable distributions, Cauchy distribution, normal distribution, Marcinkiewicz theorem.
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