模糊数值函数强Henstock积分的原函数的刻画定理  

The Characterization of the Primitives for Fuzzy Strong Henstock Integrable Functions

作　　者：贾凤玲[1] 何万生[1] 巩增泰[2] 

机构地区：[1]天水师范学院数学与统计学院,甘肃天水741001 [2]西北师范大学数学与信息科学学院,甘肃兰州730070

出　　处：《四川师范大学学报（自然科学版）》2012年第1期82-85,共4页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(10771171);甘肃省教育厅科研基金(0608-04)资助项目

摘　　要：一个实函数F如果ACG*且F'(x)=f(x)在区间[a,b]上几乎处处成立,则f在[a,b]上Hens-tock可积,且F是f的积分原函数.相反结论也成立.而模糊Henstock积分原函数并不几乎处处可导的,因此在Vitali覆盖意义下讨论模糊强Henstock积分原函数显然是不可取的.把经典实分析理论用于模糊积分理论,利用已有的内部变差概念,给出模糊数值函数强Henstock积分的原函数的完全刻画定理.A function F is ACG＊ and F′（x）= f（x） almost everywhere on ,then f is Henstock integrable on and F is the primitive of f.The reverse implication also holds.This fact is also valid for the strong Henstock integral.The primitive of fuzzy Henstock integral is not differentiable almost everywhere,it is impossible to discuss the primitive of fuzzy strong Henstock integral in sense of Vitali covering.In this paper,by applying the classical theory of real integration to fuzzy integral theory,a characterization of primitives for fuzzy strong Henstock integrable functions is obtained by using the concept of inner variation proposing by Henstock.

关 键 词：强Henstock积分 模糊数值函数 原函数 内部变差 

分 类 号：O174.1[理学—数学]