若在区间(a，b)中，函数f(x)能够表成Φ(x)一Ψ(x)的形状，而Φ与Ψ都是非减有界函数，则称f(x)在(a，b)中是有界变差的．易见两有界变差函数的和、差与积也都是有界变差的．
Φ有界变差函数 function of c-bounded variation
P次有界变差函数 functions of bounded variation of order
有界变差奇异函数 singular function of bounded variation
有界变差的区间函数 [数] interval function of bounded variation
有界变差分的区间函数 interval function of bounded variation
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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。
The paper gives the definitions of monotonic function, bounded variation function and absolute continuous function, and discusses the relationship of the three.
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。
In practice, rough variables may not be real number values, and their values may be continuous functions, bounded variation functions and so on.
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。
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.
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