Abstract
In this thesis, we study the theory of integrations for moltifunctions andgive some simple applications. The Hausdorff convergence and Kuratowski convergence for sequences of sets are investigated. A measurable selectiontheoren of Ekeland and Teman are generalized. And we prove some theorems on the convergent sequences of measurable multifunctions. Also we investigate the L -selections for multifunctions in which we establish some convergence theorems for Aumann integrals. The -spaces of multifunctions are constructed and the Fubini theorem for multifunctions of two variables is established.本論文探討集值函數的積分理論並給出一些應用的實例。首先, 我們檢視集列的兩種收斂概念- Hausdorff 意味下的收斂概念及Kuratowski意味下的收斂概念。然後建立集值函數的可測性; 推廣Ekeland 與Temam 的一個可測選擇函數的定理。在上述兩種收斂概念下, 我們驗證了可測集值函數列的極限的可測性, 接著, 我們檢視集值函數的 - 空間, 又我們證明了關於Aumann積分的種種收斂定理也證明雙變數集值函數的Fubini型定理。