Nonequivalence of Various Definitions of Differentiability Directions for Vector Measures

被引:0
作者
V. A. Romanov
机构
[1] Kirovograd State Pedagogical University,
来源
Mathematical Notes | 2002年 / 72卷
关键词
vector measure; differentiability direction; directional differentiability in various topologies; differential of vector measure;
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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.
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页码:489 / 494
页数:5
相关论文
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  • [1] Averbukh V. I.(1971)Distributions and Differential Equations in Linear Spaces. I. Differentiable Measures Trudy Moskov. Mat. Obshch. [Trans. Moscow Math. Soc.] 24 133-174
  • [2] Smolyanov O. G.(1995)On the nonequivalence of three definitions of continuous directions for vector measures Mat. Zametki [Math. Notes] 57 310-312
  • [3] Fomin S. V.(1976)On the decomposition of a measure in a linear space into a sum of H-continuous and completely H-discontinuous measures Vestnik Moskov. Univ. Ser. I Mat. Mekh. [Moscow Univ. Math. Bull.] 31 63-66
  • [4] Romanov V. A.(1977)On H-continuous measures in Hilbert spaces VestnikMosk ov. Univ. Ser. I Mat. Mekh. [Moscow Univ. Math. Bull.] 32 81-85
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