Study of generalized Kahler-Einstein metrics

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I have proved that the logarithmic plurisubharmonicity of the canonical measure on a smooth projective family of nonnegative Kodaira dimension and the smooth dependence of the canonical measure on the family. As an application, we have proven the global generation of the direct image of the pluricanonical systems. This result gives the affirmative answer to Iitaka's conjecture. The proof uses the Monge-Ampere foliation.