Choquet-like积分的一致自连续性和一致逆自连续性

任意给定非负单调集函数和非负可测函数,Choquet-like积分将确定一个新的集函数。在本文中,我们讨论了一类Choquet-like积分确定的集函数的性质。这类Choquet-like积分中伪乘的单位元不是相应伪加的幂等元。通过引入次可加性、超可加性、一致自连续和一致逆自连续概念的变体形式,我们证明了这类Choquet-like积分保持这些结构特征。这些结果将丰富Choquet-like积分的性质。

Uniform Autocontinuity and Uniform Converse-autocontinuity of Choquet-like integrals

Choquet-like integral defines a new set function for any given set function and measurable function. In this paper,we discuss the properties of set functions defined by a kind of Choquet-like integrals in which the identity element of pseudo multiplication is not an idempotent of pseudo addition. We prove that this kind of Choquet-like integrals preserves the structural characteristics by introducing the variants of null-additivity,converse-null-additi vity,uniform autocontinuity and uniform converse-autocontinuity. These conclusions can enrich Choquet-like integrals.