数学物理学报 ›› 2016, Vol. 36 ›› Issue (6): 1017-1026.

• 论文 •    下一篇

图像面积有限的集值映射

涂强, 陈文艺   

  1. 武汉市武汉大学数学与统计学院 武汉 430072
  • 收稿日期:2016-03-22 修回日期:2016-07-21 出版日期:2016-12-26 发布日期:2016-12-26
  • 作者简介:涂强,qiangtu@whu.edu.cn;陈文艺,wychencn@whu.edu.cn
  • 基金资助:

    国家自然科学基金(11131005,11301400)和中央高校基础研究基金(2014201020203)资助

Set-Valued Maps with Graphs of Finite Area

Tu Qiang, Chen Wenyi   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072
  • Received:2016-03-22 Revised:2016-07-21 Online:2016-12-26 Published:2016-12-26
  • Supported by:

    Supported by the NSFC (11131005,11301400) and the Fundamental Research Funds for the Central Universities (2014201020203)

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fF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.

关键词: 上半连续, 有界变差函数,

Abstract:

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.

Key words: Upper semi-continuous, BV function, Current

中图分类号: 

  • O174.12