歐氏空間集合級數在豪斯多夫距離下對∑AB 收斂性之研究

Euclidean Space Series of Sets Under Hausdorff Distance for ∑AB

鍾韻雯(Yun-Wen Chung)

指導教授 ： 吳裕振

中原大學/理學院/應用數學研究所/碩士(2013年)

https://doi.org/10.6840/cycu201300184

摘要

本篇論文主要對歐氏空間集合級數在豪斯多夫距離下對∑AB 收斂性
之探討, 我們對於兩個集合之乘積定義和一般的定義方式不同, 而且乘積後
的集合還是保持同樣的維度, 我們也推廣從一維度的空間到n 維度的空間,
並且找到了好幾種的充份條件如狄利克雷審斂法、Holder’s不等式和Mertens
定理之推廣, 而且我們也利用到李俊霖(2012) 所提出集合級數的絕對收斂
的一些性質和利用一些分析之技巧來完成我們的論文。

關鍵字

乘積級數 ； 歐氏空間 ； 豪斯多夫距離

並列摘要

The papers mainly on the Euclidean space collection series discussion
on convergence of ∑AB in the Hausdorff distance. Our
product of the two collections of definitions is different from general
ways. And after the product collection is also maintaining the same
dimensions. We also promote a space of dimension n-dimensional
space. And found several sufficient conditions such as Dirichlet
convergence, Holder’s generalization of the inequality and Mertens
theorem. And we also used Li Junlin (2012) made by set some
properties of the absolute convergence of series and the skills to
finish or use some prayer of our papers.

並列關鍵字

Euclidean Space ； Hausdorff Distance ； Product Series

參考文獻

[1] Apostol, T. M., (1974). Mathematical Analysis, 2nd edition, Addison-Wesley, Reading,

Massachusetts.

[2] C. Castaing and M. Valadiner, (1997). Convex Analysis and Measurable Multifunctions,

[4] Taylor, A. E. and Lay, D. C., (1980). Introduction to Functional Analysis, 2nd

[5] 李俊霖, (2012). Euclidean Space Absolutely Convergent Series of Sets Under Hausdorff