中文摘要：

为了使读者更好地理解有界变差函数全变差可加性定理，针对大多证明方法描述的模糊性，采用固定变量的方法加以详细证明，使证明过程更加清晰，也为学习深层次知识打下基础。

英文摘要：

In order to enable readers to understand better for the theorem of the additive property of total variation of the function of bounded variation accurately, a way is used of pinned variable in this paper to prove some steps in the verification compared with the original indeterminate one in most of the textbooks. Through this way, it makes the proof more clearly and also lays the foundations for learning deep knowledge of the future.