Gh-convergence of CAT(0)-spaces: stability of the Euclidean factor

We prove that if a sequence of geodesically complete CAT(0)-spaces \(X_j\) $X_j$ with uniformly cocompact discrete groups of isometries converges in the Gromov-Hausdorff sense to \(X_\infty \) $X_{\infty }$ , then the dimension of the maximal Euclidean factor splitted off by \(X_\infty \) $X_{\infty }$ and \(X_j\) $X_j$ is the same, for j big enough. In other words, no additional Euclidean factors can appear in the limit.