  We examine the stability of wireless networks whose users are distributed
over a compact space. A subset of users is called {\it admissible} when their
simultaneous activity obeys the prevailing interference constraints and, in
each time slot, an admissible subset of users is selected uniformly at random
to transmit one packet. We show that, under a mild condition, this random
admissible-set scheduling mechanism achieves maximum stability in a broad set
of scenarios, and in particular in symmetric cases. The proof relies on a
description of the system as a measure-valued process and the identification of
a Lyapunov function.
