在這篇論文中，我們會提供一個充分條件使得級數 T_n=a_{n1}*X_1+a_{n2}*X_2+...+a_{nk}*X_k+...幾近收斂，其中{X_k,k=1,2,
...}為一φ-subgaussian隨機變數數列。另外，我們會探討有關傅立葉分析的主題。實際上，我們會證明級數 a_1*X_1*cos(t+D_1)+...+a_n*X_n*cos(nt+D_n)+...,0≦t≦2π 幾近收斂到一個隨機過程 f(t),0≦t≦2π，其中{X_n,n=1,2,...}仍然為一φ-subgaussian 隨機變數數列，而{D_n,n=1,2,...}為一任意的隨機變數數列。

In this thesis we give a sufficient condition for the almost sure convergence of weighted sums of T_n=a_{n1}*X_1+a_{n2}*X_2+...+a_{nk}*X_k+... , where {X_k,k=1,2,...} be a sequence of φ-subgaussian random variables. Further-more, an application to the Fourier analysis is given. More
precisely, let {X_n,n=1,2,...} be a sequence of φ-subgauss-
ian random variables and {D_n,n=1,2,...} be an arbitrary
sequence of random variables. We consider the convergence
of the series a_1*X_1*cos(t+D_1)+...+a_n*X_n*cos(nt+D_n)+
...,0≦t≦2π to a stochastic process f(t),0≦t≦2π.

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