动态P-积分及其性质  

Dynamic P-integral and its properties

作　　者：黄江燕[1] 邹玮刚[1] 

机构地区：[1]江西理工大学理学院,江西赣州341000

出　　处：《江西理工大学学报》2012年第5期78-81,共4页Journal of Jiangxi University of Science and Technology

基　　金：江西省自然科学基金项目(2009GQS0047)

摘　　要：内P-集合XF,外P-集合XF是经典集合X动态生成的两个普通集,由内P-集合与外P-集合构成的集合对(XF,XF)就是P-集合.在P-集合的基础上,得到函数对(pF(x),pF(x))与该函数对的性质.进而给出P-积分的概念与结构,P-积分是由内P-积分(∫baPF(x)dx)与外P-积分(∫baPF(x)dx)构成的集合对,P-积分具有动态特性.文中给出了动态P-集合序定理与P-积分双中值定理,并指出P-积分是牛顿积分的动态表现形式,牛顿积分是P-积分的特例.P-积分有序定理和P-积分双中值定理.事实证明,牛顿积分中值定理是P-积分双中值定理的特例.Internal packet sets XF and outer packet sets Xr are two packet sets generated by cantor ＇ sets X. Internal packet sets Xf and outer packet sets Xr construct packet sets, on which a function （pF（x） ,pF（x））and the character of it are obtained. In order to develop the special nature of the dynamic function, the definition and construction of P- integral are given in the paper. P- integral is composed by internal packet integral and outer packet integral. Some basic properties of the dynamic integration are also discussed. A dynamic P- sets order theorem and integral double mean value theorem are presented, which point out that the integral is the dynamic performance form of the Newton integral, Newton integral is a special case of the P-integral. It is proved that Newton mean value theorem of integral is the special case of P- Integral double integral mean value theorem.

关 键 词：动态特性 P-集合 P-积分 

分 类 号：O159[理学—数学]