On a criterion for determinate moment sequences

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Attributed to Perron [2], it is obtainable only by transforming a criterion for Stieltjes determinacy due to Perron. In doing so, I find (1) not to follow from Perron's result. In this note, I shall make the proper correction to eliminate confusion caused by the error (e.g., (1) if valid would be more general than Carleman's well known criterion [l]). I also give an example to show that (1) is invalid. Symmetrization of all mass distributions with the moments pn shows that {p„} is determinate provided that there is no more than one symmetric distribution with the moments po, 0, ju2, 0, • • ■ . But the latter condition is easily shown to be equivalent to Stieltjes determinacy of the moment sequence {m2»J (not the same as Hamburger determinacy of {p2n} [4]). Perron [2] gives as a sufficient condition for Stieltjes determinacy Of {p2n}