This paper aims at finding conditions on a Hamburger or Stieltjes moment sequence, under which the change of at most a finite number of its entries produces another sequence of the same type. It turns out that a moment sequence allows all small enough variations of this kind precisely when it is indeterminate. We also show that a determinate moment sequence has the finite index of determinacy if and only if the corresponding finite number of its entries can be changed in a certain way.

中文翻译：

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汉堡和 Stieltjes 矩序列的刚性

本文旨在寻找汉堡或斯蒂尔杰斯矩序列的条件，在该条件下，最多改变其有限数量的条目会产生另一个相同类型的序列。事实证明，当矩序列不确定时，它允许这种类型的所有足够小的变化。我们还表明，当且仅当其条目的相应有限数量可以以某种方式改变时，确定矩序列具有确定性的有限索引。