本篇論文一開始，說明了一些有關σ-limit的歷史，並將σ-limit加強成一個新的極限--sσ-limit,第二節中，我們探討了一些有關sσ-limit的一些結果，第三節則是介紹sσ-limit與向量值的函數之間的關係，第四節則是證明了一個數列在reflexive Banach space 中的表現定理,最後,在第五節,我們給了一些有關sσ-limit的例子。

In this paper,we will discuss a new limit--sσ-limit. In section 2, we prove some results about sσ-limit. In section3, we discuss the sσ-limit and the vector-valued functions. In section 4, we prove the representation of sequence in a reflexive Banach space. Finally, we give some examples about sσ-limit in section 5.

1. Induction ........................1
2. Basic properties of sσ-limit ..........................3
3. sσ-limit and vector-valued functions ...............................9
4. The representation of a sequence in a reflexive Banach space..............13
5.Examples .............................................19
References .................................20

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