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1·The paper gives the definitions of monotonic function, bounded variation function and absolute continuous function, and discusses the relationship of the three.

文章给出了单调函数、有界变差函数、绝对连续函数的定义并讨论了三者之间的关系。

2·It is also proved as application that any bounded variation function can be seen as a differentiable function beside a set of arbitrary small measure.

作为应用，证明了任意有界变差函数都与某可微函数在除过测度任意小的集合外重合。

3·The cartoon component of an image is modeled by a bounded variation (BV) function; the corresponding incorporation of BV penalty terms in the variational functional leads to solve PDE equations.

图像的卡通部分是由一个有界变差(BV)函数来刻画，相应的将BV罚项合并到变分泛函中需要解偏微分方程。