Data di Pubblicazione:
2015
Citazione:
A note on a Residual Subset of Lipschitz Functions on Metric Spaces / F. Cavalletti. - In: PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY. - ISSN 0013-0915. - 58:3(2015 Oct), pp. 631-636. [10.1017/S0013091514000261]
Abstract:
Let (X, d) be a quasi-convex, complete and separable metric space with reference probability measure m. We prove that the set of real-valued Lipschitz functions with non-zero pointwise Lipschitz constant m-almost everywhere is residual, and hence dense, in the Banach space of Lipschitz and bounded functions. The result is the metric analogous to a result proved for real-valued Lipschitz maps defined on ℝ2 by Alberti et al.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Lipschitz functions; non-zero gradient; residual sets;
Elenco autori:
F. Cavalletti
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