关于点变差函数的某些性质

Some Properties or Daint-variation Function

设ｆ（ｘ）为定义于区间Ⅰ（有限或无限）上的有限实函数。任给实数δ＞０，ｘ∈Ⅰ，（ｆ）表示ｆ（ｘ）在［ｘ－δ，ｘ＋δ］上之全变差，本文中定义Ａ_ｆ＝｛ｘ，ｘ∈Ｉ，ｆ（ｘ）＜＋∞｝．研究了ｆ（ｘ）及集合Ａｆ的某些性质．

A finite real function f(x) is defined on interval Ⅰ (finite or infinite). For any real number δ>0, x∈Ⅰ, we let (f) denote the total variation of f(x) on [x-δ,x+δ] , (f) and Af= {x ,x∈Ⅰ ,f(x) < +∞} . Some properties of the function f (x) including the properties of the set A_f are discussed.