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Helson matrices are considered as linear operators on $\\ell^2(\\mathbb{N})$. By interpreting Helson matrices as Hankel matrices in countably many variables we use the theory of multivariate moment problems to show that $M(\\alpha)$ is non-negative if and only if $\\alpha$ is the moment sequence of a measure $\\mu$ on $\\mathbb{R}^\\infty$, assuming that $\\alpha$ does not grow too fast. 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