关于矩集的极值点
On the extreme points of moments sets
摘要：
给出了一个测度成为测度集（在抽象可测空间上）具有规定广义矩的极值点的充要条件，并应用于此类矩集上的极值问题;这些条件用可测空间的原子划分表示。本文还证明了，当可测空间具有适当的拓扑性质时，每个这样的极值测度都可以用k个Dirac概率测度的非负系数线性组合来充分表示，其中k是矩的限制数.证明是基本的，主要是自包含的。
英文摘要：
Necessary and sufficient conditions for a measure to be an extreme point of the set of measures (on an abstract measurable space) with prescribed generalized moments are given, as well as an application to extremal problems over such moment sets; these conditions are expressed in terms of atomic partitions of the measurable space. It is also shown that every such extreme measure can be adequately represented by a linear combination of k Dirac probability measures with nonnegative coefficients, where k is the number of restrictions on moments; moreover, when the measurable space has appropriate topological properties, the phrase "can be adequately represented by" here can be replaced simply by "is". The proofs are elementary and mainly self-contained.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
