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.
@article{bwmeta1.element.bwnjournal-article-smv115i3p277bwm,
author = {Nik Weaver},
title = {Nonatomic Lipschitz spaces},
journal = {Studia Mathematica},
volume = {113},
year = {1995},
pages = {277-289},
zbl = {0839.46014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv115i3p277bwm}
}
Weaver, Nik. Nonatomic Lipschitz spaces. Studia Mathematica, Tome 113 (1995) pp. 277-289. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv115i3p277bwm/
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