中文摘要：

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.

英文摘要：

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.