This note aims to show a uniqueness property for the solution (wheneverexists) to the moment problem for the symmetric algebra $S(V)$ of a locallyconvex space $(V, \tau)$. Let $\mu$ be a measure representing a linearfunctional $L: S(V)\to\mathbb{R}$. We deduce a sufficient determinacy conditionon $L$ provided that the support of $\mu$ is contained in the union of thetopological duals of $V$ w.r.t. to countably many of the seminorms in thefamily inducing $\tau$. We compare this result with some already known inliterature for such a general form of the moment problem and further discusshow some prior knowledge on the support of the representing measure influencesits determinacy.
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机译：本注释旨在显示局部凸空间$（V，\ tau）$的对称代数$ S（V）$的矩问题的解（只要存在）的唯一性。令$ \ mu $为代表线性函数$ L的度量：S（V）\ to \ mathbb {R} $。我们推断出$ L $的充分确定性条件，前提是$ \ mu $的支持包含在$ V $ w.r.t.的拓扑对偶的并集中。导致家庭中的许多半范数诱发$ \ tau $。我们将此结果与矩量问题的这种一般形式的一些已知文献进行比较，并进一步讨论了关于代表性度量支持的一些先验知识如何影响其确定性。
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