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Maximum likelihood methods are utilized to derive evolutionary luminosity functions for X-ray selected AGN's from the Einstein Extended Medium Sensitivity Survey. Our analysis is unique in that 1. We require our model of evolution to be consistent with physical continuity of the numbers of AGN, 2. We use maximum likelihood to determine the values of all free parameters simultaneously, and 3. We use Monte Carlo simulations to determine the absolute statistical significance of our best fit parameters. The last point corrects errors one would make if they used Komolgorov-Smirov confidence limits without considering that they have first obtained the best-fit to the free parameters. Assuming an initial power law luminosity function, we find that we require breaks at low and high luminosities. Assuming that the luminosity of an individual AGN changes with time as a power law proportional to the current AGN luminosity, we rule out power law indices of either 1.0 (the "pure luminosity evolution" case) or 1.5. Those two indices have been predicted from specific physical models. We will also discuss implications for the fraction of the X-ray background produced by AGN.
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