中文摘要：

宽度理论由于其与最优算法紧密相连，进而得以蓬勃发展，成为逼近论的重要分支之一。陈广贵和蔡斌畏（2011年）研究了无限维空间在概率框架和平均框架下的非线性逼近特征。文章继续他们的研究，考察了无限维空间在概率和平均框架下的线性逼近特征问题，进而得出了无限维空间在概率框架和平均框架下线性宽度的精确阶。

英文摘要：

The theory of width is flourish because of the closely linked with the optimal algorithm. In 2011, Chen guanggui and Cai binwei had studied the nonlinear approximation characteristic of infinite-dimensional space. In this paper, we study the linear approximation characteristic of infinite-dimensional space, and furthermore, we obtain the sharp order of linear widths of infinite-dimensional space in probabilistic setting and average setting.