Complete convergence and complete integration convergence for weighted sums of arrays of rowwise $m$-END under sub-linear expectations space

In this paper, we study the complete convergence and the complete integration convergence for weighted sums of $m$-extended negatively dependent ( $m$-END) random variables under sub-linear expectations space with the condition of $\hat{\mathbb{E}}|X{|}^p⩽C_{\mathbb{V}}(|X{|}^p)<\mathrm{\infty }$, $p>1/\alpha$ and $\alpha >3/2$. We obtain the results that can be regarded as the extensions of complete convergence and complete moment convergence under classical probability space. In addition, the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of $m$-END random variables under the sub-linear expectations space is proved.