图像面积有限的集值映射  

Set-Valued Maps with Graphs of Finite Area

作　　者：涂强[1] 陈文艺[1] 

机构地区：[1]武汉市武汉大学数学与统计学院,武汉430072

出　　处：《数学物理学报（A辑）》2016年第6期1017-1026,共10页Acta Mathematica Scientia

基　　金：国家自然科学基金(11131005;11301400);中央高校基础研究基金(2014201020203)资助~~

摘　　要：该文利用集值映射得到了一个对有界变差函数的刻画.由此证明了对任意的有闭,凸像的上半连续集值映射F,如果其图像面积有限,则存在一有界变差函数f是F的可数选择.而且F的rectifiable图像可被光滑函数图像以流意义弱逼近和图像面积强逼近.In this paper, we give a characterization of functions of bounded variation by using set-valued maps and show that for any upper semi-continuous set-valued map F with closed, convex images and graph of finite area, there exists a measurable selection of F which is a function of bounded variation. Moreover, the rectifiable graphs of such maps can be approximated weakly in the sense of currents and in area by graphs of smooth maps.

关 键 词：上半连续 有界变差函数 流 

分 类 号：O174.12[理学—数学]