Abstract
We study the projective logarithmic potential Gμ of a probability measure μ on the complex projective space Pn. We prove that the range of the operator μ⟶Gμ is contained in the (local) domain of definition of the complex Monge–Ampère operator acting on the class of quasi-plurisubharmonic functions on Pn with respect to the Fubini–Study metric. Moreover, when the measure μ has 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 on Pn.
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