A New Moment Determinacy Condition for Probability Distributions

In this paper, we propose a condition on a probability distribution that enables us to determine the distribution uniquely using all of its moments. This condition applies to both the Hamburger case (distributions on the entire real line) and the Stieltjes case (distributions on the positive half-line). The proposed condition is easily verifiable and is connected to both the Lin condition and the converse Krein condition. In addition, we provide another determinacy condition for both Hamburger and Stieltjes moment problems, which is similar to the Lin condition but does not necessitate the converse Krein condition.