凸体的P-差体度量  

p-difference body metric of convex bodies

作　　者：马梁英 

机构地区：[1]上海大学理学院,上海200444

出　　处：《应用数学与计算数学学报》2016年第3期369-375,共7页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11271244)

摘　　要：结合差体度量与L_p-Minkowski组合的定义,引入了凸体的p-差体度量,并通过p-差体度量与p-Hausdorff度量的等价性与一致不等价性的研究,证明了赋予p-差体度量的凸体空间是完备的.Combining with the difference body metric and the Lp-Minkowski com- bination, the p-difference body metric of convex bodies is introduced. By researching the equivalence and the uniformly non-equivalence between the p-difference body metric and the p-Hausdorff metric, it is proved that the convex bodies space endowed with the p-difference metric is complete.

关 键 词：凸体 p-差体度量 p-Hausdorff度量 完备性 

分 类 号：O186.5[理学—数学]