Space-division multiple-access (SDMA) systems that employ multiple antenna elements at the base station can provide much higher capacity than single-antenna-element systems. A fundamental question to be addressed concerns the ultimate capacity region of an SDMA system wherein a number of mobile users, each constrained in power, try to communicate with the base station in a multipath fading environment. In this paper, we express the capacity limit as an outage region over the space of transmission rates from the mobile users. Any particular set of rates contained within this region can be transmitted with an outage probability smaller than some specified value. We find outer and inner bounds on the outage capacity region for the two-user case and extend these to multiple-user cases when possible. These bounds provide yardsticks against which the performance of any system can be compared.