摘要
当次可加数列的一般项与其项数之比为有下界的数列时,证明了比值数列必有极限.从这一结果出发证明了,当定义在(0,+∞)上的次可加函数与其自变量之比为有界函数时,次可加函数必存在上下确界函数,并证明了其上下确界函数均为齐次线性函数.进一步地,次可加数列和次可加函数的这些性质还可推广到其相近类.
It is proved that when all the ratios of the generic term of a subaddtive sequence to its ordinal number form a lower bounded sequence,the ratio sequence must have limitation. From this, it is proved that when all the ratios of a subaddtive function defined on the interval （0, ＋∞） to the value of its variable form a bounded function, the subaddtive function must have supremum and infimum functions, which are homogeneously linear functions. Furthermore, its analogs are also investigated and some important results are derived in the paper.
出处
《江南大学学报（自然科学版）》
CAS
2006年第1期107-110,共4页
Joural of Jiangnan University (Natural Science Edition)
基金
湖南省自然科学基金项目(03JJY3014)
关键词
次可加函数
函数与自变量之比
有界函数
极限
上下确界函数
subaddtive function
ratio of function to its variable
bounded function
limitation
supremnm and infimum function
