Acta mathematica scientia,Series A ›› 2016, Vol. 36 ›› Issue (6): 1017-1026.

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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)

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

CLC Number: 

  • O174.12
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