In this note, we give sufficient conditions for the almost sure and the convergence in $\mathbb{L}^p$ of a $U$-statistic of order $m$ built on a strictly stationary but not necessarily ergodic sequence.

翻译：本文给出了严格平稳但不必遍历序列上构建的$m$阶$U$-统计量几乎必然收敛及$\mathbb{L}^p$收敛的充分条件。