单调测度的绝对连续性  

Absolute Continuity of Monotone Measures

作　　者：韦叶[1] 颜廷苏[2] WEI Ye;YAN Tingsu(Zhejiang Information Engineering School,Huzhou 313000,China;School of Science,Huzhou University,Huzhou 313000,China)

机构地区：[1]浙江信息工程学校,浙江湖州313000 [2]湖州师范学院理学院,浙江湖州313000

出　　处：《湖州师范学院学报》2022年第10期15-20,共6页Journal of Huzhou University

基　　金：浙江省教育厅科研项目(Y202044021)。

摘　　要：讨论单调测度的[E]-型、[L]-型和[R]-型3种绝对连续性与单调测度的条件[E](单调测度空间Egoroff定理成立的充分必要条件)、强序连续(单调测度空间Lebesgue定理成立的充分必要条件),以及性质(S)(单调测度空间Riesz收敛定理成立的充分必要条件)之间的关系.结果发现,两个单调测度之间的[E]-型绝对连续性与此两个测度是否满足条件[E]无关,两者是彼此独立的.[L]-型和[R]-型绝对连续性有着类似的结论.The relationships between three types(type [E], type [L] and type [R]) of the absolute continuity and the condition [E] for monotone measures are discussed. It is shown that the type-[E]absolute continuity of one monotone measure with respect to another monotone measure is independ from the condition [E] or not. The type-[L] absolute continuity and type-[R] absolute continuity have the similar assertion.

关 键 词：单调测度 绝对连续性 EGOROFF定理 

分 类 号：O171[理学—数学]