Repeated quasi-integration on locally compact spaces

被引:0
作者
Butler, Svetlana, V [1 ]
机构
[1] Univ Calif Santa Barbara, Dept Math, 552 Univ Rd, Isla Vista, CA 93117 USA
关键词
Quasi-integral; Repeated quasi-integration; Simple and almost simple quasi-integrals; Quasi-linear functional; Topological measure; DEFICIENT TOPOLOGICAL MEASURES; STATES; CONSTRUCTION; RESPECT;
D O I
10.1007/s11117-022-00864-7
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
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 equivalent conditions for a quasi-integral to be simple or almost simple. We give 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 or almost 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.
引用
收藏
页数:18
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