有界变差是函数的一个性质，它指的是总变差为有限的函数。

有界变差的理论对黎曼－斯蒂尔杰斯积分有相当的用处。

设，若一个定义于实数区间上函数是有界变差函数，则对于任意在上的划分而言，存在一正实数而言，有

其定义可推广至复数乃至于任何的欧几里德空间上。

In mathematical analysis, a function of bounded variation, also known as a BV function, is a real-valued function whose total variation is bounded (finite): the graph of a function having this property is well behaved in a precise sense. For a continuous function of a single variable, being of bounded variation means that the distance along the direction of the y-axis, neglecting the contribution of motion along x-axis, traveled by a point moving along the graph has a finite value. For a continuous function of several variables, the meaning of the definition is the same, except for the fact that the continuous path to be considered cannot be the whole graph of the given function (which is a hypersurface in this case), but can be every intersection of the graph itself with a hyperplane (in the case of functions of two variables, a plane) parallel to a fixed x-axis and to the y-axis.