Theory of Probability &Its Applications, Volume 65, Issue 3, Page 497-509, January 2020.
We have analyzed some conditions which are essentially involved in deciding whether or not a probability distribution is unique (moment-determinate) or nonunique (moment-indeterminate) by its moments. We suggest new conditions concerning both absolutely continuous and discrete distributions. By using the new conditions, which are easily checkable, we either establish new results or extend previous ones in both the Hamburger case (distributions on the whole real line) and the Stieltjes case (distributions on the positive half-line). Specific examples illustrate the results as well as the relationship between the new conditions and previously available conditions.

中文翻译：

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概率分布矩确定性的新可检查条件

概率论及其应用，第65卷，第3期，第497-509页，2020年1月。
我们分析了一些条件，这些条件实际上涉及确定概率分布是唯一的（矩确定的）还是非唯一的（矩确定的） ）。我们建议有关绝对连续和离散分布的新条件。通过使用易于检查的新条件，我们既可以建立新的结果，也可以扩展先前的结果，既可以用于汉堡案例（位于整个实线上的分布），也可以用于斯蒂尔杰斯案例（位于正半线上的分布）。具体示例说明结果以及新条件与先前可用条件之间的关系。