局部紧空间上的重拟积分
Repeated quasi-integration on locally compact spaces
摘要：
当$X$是局部紧的时，$ C_c(X)$上的拟积分（也称为拟线性泛函）是齐次正泛函，仅假设其在单生成子代数上是线性的。我们研究简单和几乎简单的拟积分，即，拟积分，其相应的紧有限拓扑措施，假设正好是两个值。我们提出了一个重复准积分的准则（即，关于拓扑测度的迭代积分）以产生准线性泛函。我们找到了二重拟积分简单的一个判据。我们描述了拓扑测度的乘积如何作用于开集和紧集。我们证明了重复拟积分中不同积分阶给出相同拟积分的充要条件是对应的拓扑测度都是测度，或者对应的拓扑测度之一是点质量的正标量倍.
英文摘要：
When $X$ is locally compact, a quasi-integral (also called a quasi-linear functional) on $ C_c(X)$ is a homogeneous, positive functional that is only assumed to be linear on singly-generated subalgebras. We study simple and almost simple quasi-integrals, i.e., quasi-integrals whose corresponding compact-finite topological measures assume exactly two values. We present a criterion for repeated quasi-integration (i.e., iterated integration with respect to topological measures) to yield a quasi-linear functional. We find a criterion for a double quasi-integral to be simple. We describe how a product of topological measures acts on open and compact sets. We show that different orders of integration in repeated quasi-integrals give the same quasi-integral if and only if the corresponding topological measures are both measures or one of the corresponding topological measures is a positive scalar multiple of a point mass.
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