中英互译

bounded variation

基本释义

In practice, rough variables may not be real number values, and their values may be continuous functions, bounded variation functions and so on.
在实际中，粗糙变量不一定是实值，他们的值有可能是连续函数、有界变差函数等等。
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。
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。

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.