检索规则说明:AND代表“并且”;OR代表“或者”;NOT代表“不包含”;(注意必须大写,运算符两边需空一格)
检 索 范 例 :范例一: (K=图书馆学 OR K=情报学) AND A=范并思 范例二:J=计算机应用与软件 AND (U=C++ OR U=Basic) NOT M=Visual
作 者:李艳红[1] LI Yan-hong(Department of Mathematics,Teacher's College,Eastern Liaoning University,Dandong,Liaoning 118003)
机构地区:[1]辽东学院师范学院数学系
出 处:《工程数学学报》2019年第6期667-677,共11页Chinese Journal of Engineering Mathematics
基 金:国家自然科学基金(61374009);辽东学院科研基金重点项目(2017ZD009)~~
摘 要:K-拟加Sugeno积分是借助于诱导算子定义的一种新型非可加积分,它在广义积分理论和一些实际应用中发挥重要作用.为克服K-拟加测度不具有可加性的先天性不足,本文建立一类新的非可加积分模型“K-拟加Sugeno积分”,从而为进一步研究非可加积分理论开辟一个新途径.一方面,在K-拟加测度空间上通过诱导算子对广义可测函数定义了K-拟加Sugeno积分,并利用该积分的解析表示讨论了广义函数列的一致可积性和一致有界性.另一方面,在K-拟加测度空间上证明了非负广义函数列的一致有界性蕴含着一致可积性,进而在K-拟加Sugeno积分意义下给出了非负广义函数列一致可积的一个充要条件.K-quasi additive Sugeno integral is a new non-additive integral defined by the induced operator,it plays an important role in the generalized integral theory and some practical applications.In order to overcome the inborn deficiency of K-quasi additive measure:without additivity,a new non-additive integral model“K-quasi additive Sugeno integral”is introduced.This provides a new way to further study the theory of non-additive integral.On the one hand,on the K-quasi additive measure space,the K-quasi additive Sugeno integral with the generalized measurable function is defined by the induced operator,and the uniform integrability and uniform boundedness of sequence of generalized functions are discussed by using the analytic representation of the integral.On the other hand,on the K-quasi additive measure space,it is proved that the uniform boundedness of a sequence of nonnegative generalized functions contains uniformly integrability,and then a sufficient and necessary condition for the uniformly integrability of the sequence of nonnegative generalized functions is given in the sense of K-quasi additive Sugeno integral.
关 键 词:诱导算子 K-拟加Sugeno积分 一致可积 一致有界
正在载入数据...
正在载入数据...
正在载入数据...
正在载入数据...
正在载入数据...
正在载入数据...
正在载入数据...
正在链接到云南高校图书馆文献保障联盟下载...
云南高校图书馆联盟文献共享服务平台 版权所有©
您的IP:216.73.216.200