We consider the determinacy problem for a distribution function $F\left(x\right)$, $x\in \mathbb{R}$, by mixed data consisting of partial information given on $F$ and knowing its finitely many moments. Necessary and sufficient conditions for solvability of the problem are derived. Essential is the established one-to-one correspondence between the Hamburger moment problem with finitely many moments and a discrete positive Borel measure concentrated at finitely many points on the real axis.

中文翻译：

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在有限多个时刻确定具有有限多个质点的分布的确定性

我们考虑分布函数的确定性问题 $F（X）$， $X\in \mathbb{[R}$，由混合数据组成，这些数据由 $F$并知道它的有限时刻。得出了解决问题的必要和充分条件。重要的是在有限个矩的汉堡矩问题和集中在实轴上有限个点上的离散正Borel测度之间建立的一对一对应关系。