本文主要是探討在使用要求較寬的函數列${phi_{n},ngeq 1}$之下,
Dr. Chung's
型式的強大數法則對於取值於Banach空間中的獨立的隨機變數${X_{n},ngeq1}$與列獨立的隨機矩陣${X_{ni},
1leq ileq k_{n}, ngeq 1
}$仍可成立的所需條件.

Let $mathcal{B}$ be a separable Banach space. In this thesis, it is shown that the Chung's strong law of large numbers
holds for a sequence of independent $mathcal{B}$-valued random
elements and an array of rowwise independent $mathcal{B}$-valued
random elements under some weaker assumptions by using more
generalized functions $phi_{n}$'s.

1. Introduction--------------------------------------------------1
2. Preliminaries-------------------------------------------------2
3. Main result
3.1 For random elements in Rademacher type p Banach space-----11
3.2 For B-valued random elements in L^P-----------------------16
References-------------------------------------------------------21

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鞅與Banach空間幾何學