A theorem on nested Matrosov functions is presented for time-varying stochastic, set-valued discrete-time systems satisfying mild regularity conditions. It establishes sufficient conditions for uniform strong global recurrence of an open, bounded set. In general Matrosov functions are required to satisfy less rigid requirements than typical Lyapunov functions that satisfy a strict decrease condition along trajectories. (C) 2013 Elsevier Ltd. All rights reserved.