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It is shown that geodesics in the space of K\"ahler potentials can beuniformly approximated by geodesics in the spaces of Bergman metrics. Twoimportant tools in the proof are the Tian-Yau-Zelditch approximation theoremfor K\"ahler potentials and the pluripotential theory of Bedford-Taylor,suitably adapted to K\"ahler manifolds.Comment: 25 pages, no figure, minor misprints correcte

The Monge-Ampère operator and geodesics in the space of Kähler potentials