| Rm上Banach-值函数的强McShane积分 |
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| 引用本文： | 叶国菊,李秉彝.Rm上Banach-值函数的强McShane积分[J].数学研究,2004,37(3):250-258. |
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| 作者姓名： | 叶国菊 李秉彝 |
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| 作者单位： | 1. 河海大学理学院,南京,210098
2. 新加坡南洋理工大学国立教育学院,新加坡,637616 |
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| 基金项目： | ScienceFoundationofHehaiUniversity |
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| 摘 要： | 在本文中,我们定义和研究了I0Rm到Banach空间X中函数的强McShane积分,直接证明了强Mcshane积分与Bochner积分是等价的,McShane积分与强Mcshane积分等价当且仅当Banach空间X有限维.
从而部分地回答了R.A.Gordon的一个公开问题.
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| 关 键 词： | 强Mcshane积分 Mcshane积分 Bochner积分 |
The Strong McShane Integral of Banach-valued functions defined on Rm |
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| Abstract.The Strong McShane Integral of Banach-valued functions defined on Rm[J].Journal of Mathematical Study,2004,37(3):250-258. |
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| Authors: | Abstract |
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| Abstract: | In this paper we define and study the strong McShane integral of functions mapping a compact interval I 0 in R m into Banach spaces X. We directly prove that the strong McShane integral and the Bochner integral are equivalent, and the McShane integral and the strong McShane integral are equivalent if and only if the Banach spaces are finite dimensional. This partially gives a positive answer to an open problem of R.A.Gordon. |
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| Keywords: | strong McShane integral McShane integral Bochner integral |
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