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摘要

We study the projective logarithmic potentialGμof a probability measureμon the complex projective spacePn. We prove that the range of the operatorμ?Gμis contained in the (local) domain of definition of the complex Monge–Ampère operator acting on the class of quasi-plurisubharmonic functions onPnwith respect to the Fubini–Study metric. Moreover, when the measureμhas no atom, we show that the complex Monge–Ampère measure of its logarithmic potential is an absolutely continuous measure with respect to the Fubini–Study volume form onPn.