令 f∶I⊆R→R 是有界的Lebesgue可積函數，g∶[a,b]→I 是一個連續函數，且對所有 n∈N，{q_i (n)∶1≤i≤n}  是一個正實數序列。
我們定義下列序列：
A_n (f,g;q)∶=  1/(b-a)^n  ∫_([a,b]^n)f((q_1 (n)g(x_1 )+⋯+q_n (n)g(x_n ))/Q_n )  dx，
這裡 Q_n∶=∑_(i=1)^n〖q_i (n) 〗  ，dx=dx_1⋯dx_n  。
　　我們探討序列 A_n (f,g;q)的收斂及估計。

Let f∶I⊆R→R be a bounded Lebesgue integrable function, g∶[a,b]→I be continuous function, and for each n∈N, {q_i (n)∶1≤i≤n} is a sequence of positive real numbers. 
We define the sequence:
A_n (f,g;q)∶=  1/(b-a)^n  ∫_([a,b]^n)f((q_1 (n)g(x_1 )+⋯+q_n (n)g(x_n ))/Q_n )  dx，
where Q_n=∑_(i=1)^n〖q_i (n) 〗, dx=dx_1⋯dx_n. 

    We investigate the properties of convergence and estimation of the sequence A_n (f,g;q).

第一章  前言………………………………………………1
第二章  一些與凸函數相關的多重積分序列的探討……7
     2-1定義與凸函數相關的多重積分序列………10
     2-2序列收斂結果………………………………19
     2-3序列的估計…………………………………22
參考文獻……………………………………………………34

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