Summary: In [Rend. Semin. Mat. Univ. Padova 24, 84–92 (1955; Zbl 0064.35704)], G. Darbo used the measure of noncompactness to investigate operators whose properties can be characterized as being intermediate between those of contraction and compact operators. In this paper, we apply the Darbo’s fixed point theorem for solving infinite system of linear equations in some sequence spaces.