中文摘要：

本文讨论由L^2深度修正得到的L^2深度相应的样本深度的性质，得到了样本深度的相合性和渐近正态性，并证明了它在任意紧集上的一致相合性．最后，基于上述性质简要讨论了样本深度等高的一些性质．

英文摘要：

As a competitive depth,L^2-depth is modified from L^2-depth. Some basic properties of L^2 sample depth are discussed. The consistency and asymptotic： normality of sample depth are derived. The uniform consistency of sample depth on any compact set is also proved. Based on the above-mentioned properties, results for contours of sample depth are given in brief.