ABSTRACT. We prove that a complex Lindenstrauss space whose unit ball has at least one extreme point is isometric to the space of complex valued continuous affine functions on a Choquet simplex. If X is a compact Hausdorff space and A CCçJLX) is a function space then A is a Lindenstrauss space iff A is selfadjoint and Re A is a real Lindenstrauss space.
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