Nonequivalence of various definitions of differentiability directions for vector measures

被引:0
作者
Romanov, VA
机构
[1] Kirovograd State Pedagogical University,
关键词
vector measure; differentiability direction; directional differentiability in various topologies; differential of vector measure;
D O I
10.1023/A:1020532311900
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
It is proved that the definitions of differentiability directions for vector measures in various topologies, namely, the topology of convergence on a system measurable sets, the topology of convergence with respect to semivariation, and the topology of convergence in variation, are generally pairwise nonequivalent. It is also proved that, for measures with values in a Banach space with the Radon-Nikodym property, these definitions are equivalent.
引用
收藏
页码:489 / 494
页数:6
相关论文
共 5 条
  • [1] [Anonymous], 1971, T MOSK MAT OBS
  • [2] DALETSKII YL, 1983, MEASURES DIFFERENTIA
  • [3] ROMA G, 1977, FARMACO-ED SCI, V32, P81
  • [4] ROMANOV VA, 1976, VESTNIK MOSKOV U IMM, V31, P63
  • [5] ROMANOV VA, 1995, MAT ZAMETKI, V57, P310