歐氏空間之集合級數豪斯多夫距離下之柯西並 項審斂法

Euclidean Space Cauchy Condensation Test for Series of Sets Under Hausdorff Distance

黃惠玲(Hui-Ling Huang)

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/cycu201200166

摘要

討論級數收斂性在分析課程是相當重要的, 所以此篇論文研究柯西並項審斂法, 而柯西並項審斂法是說只要在某些條件下, 只要取其中子數列的級數之收斂性會和原本級數收斂性是一致的. 我們也把它推廣到歐氏空間之集合級數, 並且在豪斯多夫距離下會有跟一維度相同之結果, 並且我們也提供了一個例子說明, 交錯級數審斂法是無法被推廣.

關鍵字

集合級數 ； 柯西並項審斂法

並列摘要

To discussing the series convergence the course of analysis is important, so that the mainly research in this paper is Cauchy condensation test. And Cauchy condensation test under smoe conditions, the convergence of series is consistent as the convergence of subseries. We are also extend it to the Euclidean space for series of sets, and under the Hausdorff distance will have an one-dimension with the same result, and we also provide an example, that the alternating series test can not be extended.

並列關鍵字

Series of sets ； Cauchy condensation test

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, 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.

[5] 徐浩鐘, (2010). Ratio Test for Series of Sets, 中原大學, 碩士論文.