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Nonatomic Lipschitz spaces. (English) Zbl 0839.46014

Summary: We abstractly characterize Lipschitz spaces in terms of having a lattice-complete unit ball and a separating family of pure normal states. We then formulate a notion of “measurable metric space” and characterize the corresponding Lipschitz spaces in terms of having a lattice complete unit ball and a separating family of normal states.

MSC:

46B42 Banach lattices
46E05 Lattices of continuous, differentiable or analytic functions
46E15 Banach spaces of continuous, differentiable or analytic functions
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