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Given a collection of K\"ahler forms and a continuous weight on a compactcomplex manifold we show that it is possible to define natural new notions ofextremal potentials and equilibrium measures which coincide with classicalnotions when the collection is a singleton. We prove two regularity results andset up a variational framework. Applications to Fekete points are treatedelsewhere.

Extremal potentials and equilibrium measures associated to collections of K\"ahler classes