集函数过程与Frechet空间的核性

集函数过程与Frechet空间的核性 THE PROCESSES OF SET FUNCTIONS AND NUCLEARITY IN FRECHET SPACES 刘培德 Liu Peide first-author 记M（Σ,E）是定义在代数Σ上取值于Frechet空间E的有界变差有限可加集函数全体。对于递增子代数列（ n ）,定义集函数渐近鞅。本文讨论了M（Σ,E）上的两种拓扑,与（ n ）适应的集函数过程成为渐近鞅的等价条件,渐近鞅的Riesz分解,变差拓扑下的收敛性及其导函数序列的a.e收敛性,上述请条件与空间E的核性之间的关系。 Denote by M（∑, E） finitely additive set functions of bounded variation, which defined on a field ∑ with values in Frechet space E. For a increasing Sequence（g n ） of Subfields of ∑, we introduce the amart of set functions. we discuss two topologies on M（∑, E） and give some equivalent Conditions that a processe of set functions becoms amart. For the amart, we discuss its Riesz decomposition and Convergence in Variation-topology and Convergence of the sequence of its Radon-Nikodym derivations. Using these, we give some characterizations of nuclear Freehet spaces. 向量测度 渐近鞅 Frechet空间 核性 Vector measure Amart Frechet Space Nuelearity 1987-04-01 2021-04-01 4