关于函数的原函数与可积性关系的讨论  

On the Relationship between Primitive Functions and Integrality of Functions

作　　者：银建华[1] 

机构地区：[1]昌吉学院数学计算机系,昌吉831100

出　　处：《新疆师范大学学报（自然科学版）》2002年第3期12-14,共3页Journal of Xinjiang Normal University(Natural Sciences Edition)

摘　　要：本文举例说明了可积函数未必存在原函数 ,而有原函数的函数未必可积。文中定理 2推广了华东师范大学的数学分析中的定理 10 .17,举例说明了其逆命题不成立。定理 3给出了其逆命题成立的条件。This article tries to illustrate the possibility that integrable functions may not necessarily involve primitive functions and functions involving primitive functions may not necessarily be integrable.Theorem 2 extends the application of Theorem 10.17 applied in Mathematics Analysis which is adopted as the textbook by East China Normal University and proves its converse proposition untenable.Theorem 3 puts forward the conditions,which makes its converse proposition tenable.\;

关 键 词：原函数 可积性 函数可积 数学分析 可积函数 导函数 价值性定理 逆命题 

分 类 号：O174.1[理学—数学]