隨機集合是隨機變數和隨機元素的推廣但是更加抽象複雜。在本論文中，我們研究了以集合為索引的隨機集合部分和的強大數法則問題，並獲得了對大數法則運作的更深刻理解，對象分別是隨機緊緻集合和隨機閉集合。我們以Hausdorf metric作為收斂概念證明了針對隨機緊緻集合的以集合為索引的強大數法則。並推廣到隨機閉集合，我們在Mosco收斂和Wijsman收斂概念下證明相關以集合為索引的強大數法則。

Random sets are a generalization of random variables and random elements but are much more abstract and complicated. In this thesis, we study a problem of the strong law of large numbers (SLLN) for random set partial sum processes indexed by sets, which gives a deeper insight into how the SLLN behaves. We establish the set indexed SLLN for random compact sets with the convergence induced by the Hausdorff metric and extend the set indexed SLLN to random closed sets with respect to Mosco convergence and Wijsman convergence.

Abstract----------------------------------------------i
摘要--------------------------------------------------ii
Acknowledgements
1 Introduction----------------------------------------1
1.1 A Glimpse-----------------------------------------1
1.2 Goal----------------------------------------------2
1.3 Structure and Notations---------------------------2
2 Preliminaries---------------------------------------4
2.1 Random Sets and Their Expectations----------------4
2.2 Support Function----------------------------------8
2.3 SLLN for Banach Space-Valued Random Elements------10
2.4 Convergence Concepts------------------------------11
3 Main Theorems---------------------------------------13
3.1 Set-Indexed SLLN for Random Compact Sets----------14
3.2 Set-Indexed SLLN for Random Closed Sets-----------19
Reference---------------------------------------------25

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