| 在n维赋范空间中单位球体积及其渐进性质 |
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| 引用本文： | 黄智悦,何斌吾.在n维赋范空间中单位球体积及其渐进性质[J].上海大学学报(英文版),2008,12(2):107-109. |
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| 作者姓名： | 黄智悦 何斌吾 |
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| 作者单位： | HUANG Zhi-yue（Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China）
HE Bin-wu（Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China） |
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| 摘 要： | Let Bnp={x ∈ Rn‖|x ‖p≤l} be the unit ball ofp norm in the n-dimensional normed space p. The formula for the volume of Bnp was obtained and its asymptotic properties were found out as n→∞and p→∞.
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| 关 键 词： | unit ball normed space volumes gamma function asymptotic properties. 赋范空间 单位 球体积 渐进性质 asymptotic properties normed space the unit ball formula volume |
| 收稿时间： | 2006-06-28 |
| 修稿时间： | 2006年6月28日 |
Volume of unit ball in an n-dimensional normed space and its asymptotic properties |
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| Zhi-yue Huang,Bin-wu He.Volume of unit ball in an n-dimensional normed space and its asymptotic properties[J].Journal of Shanghai University(English Edition),2008,12(2):107-109. |
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| Authors: | Zhi-yue Huang Bin-wu He |
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| Institution: | Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China |
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| Abstract: | Let B
p
n
= {x ∈ R
n
|∥x∥
p
⩽ 1} be the unit ball of p norm in the n-dimensional normed space  . The formula for the volume of B
p
n
was obtained and its asymptotic properties were found out as n → ∞ and p → ∞.
Project supported by the Science Foundation of Shanghai Municipal Commission of Education (Grant No.24667). |
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| Keywords: | unit ball normed space volumes gamma function asymptotic properties |
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