Complex Monge-AmpÃ¨re Measures of Plurisubharmonic Functions with Bounded Values Near the Boundary We give a characterization of bounded plurisubharmonic functions by using their complex Monge-Amp\ere measures. This implies a both necessary and sufficient condition for a positive measure to be complex Monge-Amp\ere measure of some bounded plurisubharmonic function. Categories:32F07, 32F05