We give a simple proof of the Cafiero theorem based on a matrix method approach in the form of Lemma 2.4 in the $\sigma$-additive context. Based on a version of Drewnowski lemma for an SCP-ring we obtain an extension of Cafiero theorem for exhaustive finitely additive set functions defined on an SCP-ring. As consequences, the well-known Nikodym and Brooks-Jewett convergence theorems are obtained.