  In this paper the stability theorem of Borkar and Meyn is extended to include
the case when the mean field is a differential inclusion. Two different sets of
sufficient conditions are presented that guarantee the stability and
convergence of stochastic recursive inclusions. Our work builds on the works of
Benaim, Hofbauer and Sorin as well as Borkar and Meyn. As a corollary to one of
the main theorems, a natural generalization of the Borkar and Meyn Theorem
follows. In addition, the original theorem of Borkar and Meyn is shown to hold
under slightly relaxed assumptions. Finally, as an application to one of the
main theorems we discuss a solution to the approximate drift problem.
