导数作为测度

导数为零，那么在连通分支内为常数.
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范数

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在这个范数下，为Banach空间 （Function BVFP -p121）

紧嵌入

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Reduce boundary

定义如下
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从定义中可以看出，对于边界充分光滑（可以定义外法向）的集合，边界都是Reduce Boundary.
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一个有用的上极限
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参考资料

https://encyclopediaofmath.org/wiki/Function_of_bounded_variation#Functions_of_several_variables
有界变差函数百科

Function BVFP
Ambrosio, Luigi; Fusco, Nicola; Pallara, Diego Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York, 2000. xviii+434 pp. ISBN: 0-19-850245-1

@book {MR1857292, AUTHOR = {Ambrosio, Luigi and Fusco, Nicola and Pallara, Diego}, TITLE = {Functions of bounded variation and free discontinuity problems}, SERIES = {Oxford Mathematical Monographs}, PUBLISHER = {The Clarendon Press, Oxford University Press, New York}, YEAR = {2000}, PAGES = {xviii+434}, ISBN = {0-19-850245-1}, MRCLASS = {49-02 (49J45 49K10 49Qxx)}, MRNUMBER = {1857292}, MRREVIEWER = {J. E. Brothers}, }