集合級數在豪斯多夫距離下之 Raabe’s 審斂法

Raabe’s Test for Series of Sets Under Hausdorff Distance

陳怡青(Yi-Ching Chen)

指導教授 ： 吳裕振

中原大學/理學院/應用數學研究所/碩士(2012年)

https://doi.org/10.6840/cycu201200160

摘要

我們知道探討級數之收斂性, 是在分析中重要的課程, 本篇論文主要在研究集合級數在豪斯多夫距離下之Raabe’s 審斂法, 而此論文的主要結果, 在Banach 空間下之集合級數對於Raabe’s 審斂法之收斂部份是成立, 但在發散部份, 我們必須在歐氏空間下才可得到Raabe’s 審斂法之發散部份, 而此結果在本篇論文有詳細的探討.

關鍵字

豪斯多夫距離 ； Raabe’s 審斂法 ； 集合級數

並列摘要

It is known to discuss the convergence of the series is an important subject in the analysis. In this paper, we will discuss the ”Euclidean Space Raabe’s Test for Series of Sets Under Hausdorff Distance”. The main result is that, the convergence of Raabe’s test is right for series of sets under Banach space. But the divergence of Raabe’s test must found in Euclidean space and these results will be introduced in the following statements.

並列關鍵字

Series of sets ； Raabe’s Test ； Hausdorff distance

參考文獻

[1] C. Castaing and M. Valadier, (1997). Convex Analysis and Measurable Multifunctions, Lecture Note in Math 580, springer-verlag.

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

[4] 李俊霖, (2012). Euclidean Space Absolutely Convergent Series of Sets Under Hausdorff Distance, 中原大學, 碩士論文.

參考文獻

[2] Knopp, K., (1948). Theory and Application of Infinite Series, 2nd edition, R. C. Young, translator, Hafner, New York.