弧长公式成立的充要条件  

The Sufficient and Necessary Conditions for the Formula of Arc Length

作　　者：王磊杰[1] 

机构地区：[1]文山学院数理系,云南文山663000

出　　处：《文山学院学报》2012年第6期45-46,共2页Journal of Wenshan University

摘　　要：连续曲线不一定可求长,连续曲线可求长当且仅当它的参数表示是有界变差的,但弧长未必能用公式表达,利用勒贝格积分的基本理论证明绝对连续是弧长可用公式计算的充要条件。Continuous curve may not be rectifiable. A curve is rectifiable, if and only if its parameter representation is bounded variation, but in general the arc length could not be formulated, and we proves by Lebesgue Integral Theory that absolutely continuous is the sufficient and necessary condition for the formula of arc length.

关 键 词：可求长曲线 弧长 绝对连续 

分 类 号：O172.2[理学—数学]