几何测度空间基的研究

陈方维

数学学报 ›› 2013, Vol. 56 ›› Issue (3) : 419-426.

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数学学报 ›› 2013, Vol. 56 ›› Issue (3) : 419-426. DOI: 10.12386/A2013sxxb0042
论文

几何测度空间基的研究

    陈方维
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On Bases of Space of Geometric Measures

    Fang Wei CHEN
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文章历史 +

摘要

研究了几何测度空间中的基本对称函数μ0, μ1,..., μn和内蕴体积函数V0,V1,..., Vn,证明了Ln上连续不变赋值函数空间中由基本对称函数构成的基{μ0, μ1,..., μn}和由内蕴体积函数构成的基{V0,V1,..., Vn}(或均质积分构成的基{W0,W1,..., Wn})等价.

Abstract

In this paper, the elementary symmetric functions μ0, μ1,..., μn and the intrinsic volumes V0,V1,..., Vn are investigated. We show that the elementary symmetric function basis {μ0, μ1,..., μn} and the intrinsic volume basis {V0,V1,..., Vn} defined on Ln (also the quermassintegral basis {W0,W1,..., Wn}) are equivalent.

关键词

几何测度 / 内蕴体积 / 基本对称函数 / 赋值函数 / 均质积分

Key words

geometric measure / intrinsic volume / elementary symmetric function / valuation / quermassintegral

引用本文

导出引用
陈方维. 几何测度空间基的研究. 数学学报, 2013, 56(3): 419-426 https://doi.org/10.12386/A2013sxxb0042
Fang Wei CHEN. On Bases of Space of Geometric Measures. Acta Mathematica Sinica, Chinese Series, 2013, 56(3): 419-426 https://doi.org/10.12386/A2013sxxb0042

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基金

国家自然科学基金资助项目(11161007, 11101099);贵州省科学技术基金资助项目([2010]2242)

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