歐氏空間在豪斯多夫距離下集合級數托普利茲
審斂法

本篇論文主要研究是把一維度托普利茲審斂法推廣到歐氏空間高維度之集合級數, 其距離我們用到的是豪斯多夫距離, 但在集合之加法上aA+bA 不一定等於(a + b)A , 因此我們必須修改托普利茲其中一個條件, 並且成功推廣到集合級數之類似托普利茲審斂法, 此證明過程相當複雜, 我們利用到一些分析技巧, 如柯西序列、三角不等式以及極限的定義等, 逐步完成了我們的證明。

關鍵字

集合級數；豪斯多夫距離；歐氏空間；托普利茲審斂法

並列摘要

In this thesis, we research Toeplitz Test for promotion to the Series of Sets of high-dimensional Euclidean Space. The distance we use is called the Hausdorff distance. But on the addition of the sets, aA+bA is not necessarily equal to(a+b)A, so we have to modify one of the conditions of Toeplitz Test, and therefore it is promoted to similar Toeplitz Test for Series of Sets successfully. This proving process is extremely complex, we use some analysis techniques, like Cauchy sequence, the triangle inequality and the definition of the limit and so on, to complete our proof gradually

並列關鍵字

Hausdorff Distance ； Euclidean Space ； Toeplitz Test ； Set Series

參考文獻

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

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

[4] 黨宥寧, (2009). Asymptotic Behavior of Set Dynamical Systems, 中原大學, 碩士論

[5] 袁重雄, (2010). Absolutely Convergent Series of Sets, 中原大學, 碩士論文.

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

國際替代計量

歐氏空間在豪斯多夫距離下集合級數托普利茲審斂法

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