【摘要】 <正> Bruckner在中证明了[a,b]上点点可导的函数,其导函数的连续点全体是G集,而任意给出一个G_t型集,则存在着[a,b]上点点可导的函数,其导函数的连续点全体等于该集合,从而解决了导函数的连续点的分布问题,但并未解决导函数的近似连续点的分布问题,只得到“导函数的非近似连续点全体为勒贝格零集”的结论。更多还原

【Abstract】 In this papers a characterization for the appsoximate continuity set of derivatvies is given.This problem was proposed py Brucker in [1],Theorem Let x)be a real differentiable function on [a,b],and let f’(x) be it’s derivative.Then the approximate continuity set F of f’(x)can be expressed asfor a system of subintervals(aij,bij) of (a,b),they are dis;oint in j.Here E∪j(aij,bij)is the union of point setsandamd m be the Lebesgue measure.Conversely,for any set F given as (*) there is a real function f(x) on [a,b] which is differentiate and the approximate continuity set of f is F.更多还原