In chapter 2 there are four goals : the first is to investigate some geometric properties of h - caccioppoli sets , the second is to characterize the discontinuous set su and jump set ju of u bvh ( ) , the third is to study pointwise behavior of u bvh ( ) and our effort is concentrated on showing approximate differentiability of u in the sense of pansu ' s , while the last and the most important is to show that dhu with u bvh ( ) as a radon measure can be split into three parts ( absolutely continuous part , jump part and cantor part , respectively ) just like the derivative of a bv function in the setting of euclidean space 第二章有四个目标：一是讨论h - caccioppoli集的若干几何性质，二是刻画h -有界变差函数的近似不连续点集和跳跃点集的特征，三是研究u bv _ h ( )的逐点行为，我们集中讨论u在pansu意义下的近似可微性，最后也是最重要的目标我们证明对u bv _ h ( ) ， d _ hu作为radon测度能够分解成绝对连续部分、跳跃部分和cantor部分之和。
