山东大学学报（理学版）
山東大學學報（理學版）
산동대학학보（이학판）
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
2015年
8期
62-71
,共10页
集值函数%集值测度%Choquet 积分
集值函數%集值測度%Choquet 積分
집치함수%집치측도%Choquet 적분
set-valued functions%multisubmeasures%Choquet integral
按照集值积分的经典定义方法，不可避免地涉及集值函数和集值测度两方面的选择问题。本文利用集值函数关于非可加测度的实值 Choquet 积分，定义和讨论了集值函数关于非可加集值测度的 Choquet 积分，并刻画了其原函数性质。结果表明，弱零可加性、零可加性、凸零可加性、伪度量性质以及 Darboux 性质在其不定积分中均可遗传到其原函数中。
按照集值積分的經典定義方法，不可避免地涉及集值函數和集值測度兩方麵的選擇問題。本文利用集值函數關于非可加測度的實值 Choquet 積分，定義和討論瞭集值函數關于非可加集值測度的 Choquet 積分，併刻畫瞭其原函數性質。結果錶明，弱零可加性、零可加性、凸零可加性、偽度量性質以及 Darboux 性質在其不定積分中均可遺傳到其原函數中。
안조집치적분적경전정의방법，불가피면지섭급집치함수화집치측도량방면적선택문제。본문이용집치함수관우비가가측도적실치 Choquet 적분，정의화토론료집치함수관우비가가집치측도적 Choquet 적분，병각화료기원함수성질。결과표명，약령가가성、령가가성、철령가가성、위도량성질이급 Darboux 성질재기불정적분중균가유전도기원함수중。
It is inevitable for the problem how to deal with two aspects of selections for a set-valued function and a mul-tisubmeasure according to the classical definition method of the set-valued integral.The Choquet integral of a set-valued function with respect to a multisubmeasure is defined and discussed by using the real-valued Choquet integral of the set-valued function with respect to the non-additive measure,and some basic properties are characterized.It shows that a lot of characters could be well kept to their primitives such as the weakly null-additive,null-additive,converse null-addi-tive,the pseudometric property and the Darboux property,and so on.
