On topological properties of the Choquet weak convergence of capacity functionals of random sets
- 作者：S. Dhompongsa ; A. Kaewkhao ; S. Saejung
- 关键词：Random closed set ; Capacity functional ; Choquet integral ; Choquet weak convergence
- 刊名：Information Sciences
- 出版年：2007
- 期刊代码：62_00200255
- 类别：cp
- 出版时间：15 April 2007
- 卷：177
- 期：8
- 页码：1852-1859
- 文件大小：175 K
摘要
In view of the recent interests in random sets in information technology, such as models for imprecise data in intelligent systems, morphological analysis in image processing, we present, in this paper, some contributions to the foundation of random set theory, namely, a complete study of topological properties of capacity functionals of random sets, generalizing weak convergence of probability measures. These results are useful for investigating the concept of Choquet weak convergence of capacity functionals leading to tractable criteria for convergence in distribution of random sets. The weak topology is defined on the space of all capacity functionals on . We show that this topological space is separable and metrizable.