Singular parts of pluriharmonic measures
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 22, Tome 217 (1994), pp. 54-58
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A measure $\mu$ defined on the complex sphere $S$ is called pluriharmonic if its Poisson integral is a pluriharmonic function (in the unit ball of $\mathbb C^n$). А probability measure $\rho$ is called representing if $\int_Sf\,d\rho=f(0)$ for all $f$ in the ball algebra. It is shown that singular parts of pluriharmonic measures and representing measures are mutually singular. Bibliography: 5 titles.