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We define a multivariate Cauchy distribution using a probability density function; subsequently, a Ferguson's definition of a multivariate Cauchy distribution can be viewed as a characterization theorem using the characteristic function approach. To clarify this characterization theorem, we construct two dependent Cauchy random variables, but their sum is not Cauchy distributed. In doing so the proofs depend on the characteristic function, but we use the cumulative distribution function todoi:10.5351/csam.2014.21.2.183 fatcat:tcycen3tbzdtlnex5x6vtopahy