單調的集值序列

Monotonic Sequences of Sets

廖安琪(An-Ci Liao)

指導教授 ： 李金城

中原大學/理學院/應用數學研究所/碩士(2010年)

https://doi.org/10.6840/cycu201000291

摘要

本論文主要是要探討單調集值序列的收斂情形。首先，先定義Hausdorff距離的意義和符號，再探討一些相關的性質。
在最後一節中，我們嘗試在Hausdorff距離之下，探討單調集值序列的收斂情形。假設集合是非空的緊緻集，集值序列在遞減的情況下我們可以證明必收斂至一非空的緊緻集，在遞增且包含於一緊緻集的情況下亦可證明必收斂至一非空的緊緻集。

關鍵字

集值序列 ； Hausdorff距離 ； 單調性

並列摘要

The subject of this paper is talking about the convergence of monotonic sequence of sets. We first define the meaning and symbol of Hausdorff distance then proceed to show some related properties and theorems.
In the last section, we try to discuss the convergence of monotonic sequence of sets under Hausdorff distance. If the sets are nonempty compact sets, we prove that, when the sequence of sets is decreasing, it must converges to a nonempty compact set and that, when it is increasing and included in a fixed compact set, it must converges to a nonempty compact set.

並列關鍵字

Sequence of sets ； Hausdorff distance ； Monotonicity

參考文獻

[1] C. Castaing and M. Valadier (1997). Convex Analysis and Measurable Multifunctions. Lecture Notes in math 580, Springer-Verlag.

[2] 許元銘 2009 Set － Valued Bernstein Polynomials, 中原大學, 碩士論文.

[3] 陳奕豪 2009 Set － On the Set-valued trigonometric-polynomial, 中原大學, 碩士論文.