网测度及应用  

Net Measure and Its Applications

作　　者：姚蓓[1] 冯志刚[1] 柳艳[1] 

机构地区：[1]江苏大学理学院,镇江212013

出　　处：《大学数学》2007年第3期96-99,共4页College Mathematics

摘　　要：给出了n-进制网测度一个具体的定义,并证明了它的一些性质如:外测度、度量外测度.给出网测度的质量分布原理,证明了它与Hausdorff测度等价,并计算了直线上的三分Cantor集和Sierpinski地毯的网测度.A detailed definition of n-net measure is presented, and some of its basic properties, such as outer measure and distant measure, are validated. Furthermore, we propose the mass distribution principle of net measure, and prove the net measure is equivalent to the Hausdorff measure. Finally, the net measures of third Cantor set and Sierpinski carpet are calculated.

关 键 词：网测度 HAUSDORFF测度 三分CANTOR集 SIERPINSKI地毯 

分 类 号：O174.12[理学—数学]