Closed form approximations of the outage capacity and the mutual information between the in- and outputs of a multi-input, multi-output (MIMO) narrowband system in the presence of correlated fading are considered. First, the limiting distribution of the squared singular values of the channel matrix is derived as the number of antennas at either the transmit or receive site increases. Spatial correlation is allowed according to a realistic stochastic channel model and correlation is allowed between the transmitted signals. The derived limiting distribution has the advantage of being closed form while simulations indicate that it provides a reasonable approximation of the true distribution also for realistic antenna array sizes. Second, the channel outage capacity is derived from the limiting distribution above for the case when the number of transmit antennas is large. The resulting outage capacity has a simple form and allows for spatially correlated channel elements as well as correlation among the transmitted signals. Results from simulations and channel measurements are presented that indicate that the derived expression provides an accurate approximation of the true channel outage capacity for a wide range of realistic system conditions.