Given a sequence of functions fn converging in some topology to a function f, in general the 0-level set of fn does not give a good approximation of the one of f. In this paper we show that, if we consider an appropriate perturbation of the 0-level set of fn, we get a sequence of sets converging to the 0-level set of f, where the type of set convergence depends on the type of convergence of fn to f.

A note on convergence of level sets / Camilli, Fabio. - In: ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN. - ISSN 0232-2064. - STAMPA. - 18:(1999), pp. 3-12.

A note on convergence of level sets

CAMILLI, FABIO
1999

Abstract

Given a sequence of functions fn converging in some topology to a function f, in general the 0-level set of fn does not give a good approximation of the one of f. In this paper we show that, if we consider an appropriate perturbation of the 0-level set of fn, we get a sequence of sets converging to the 0-level set of f, where the type of set convergence depends on the type of convergence of fn to f.
Perturbed level sets; set convergence; capacity
01 Pubblicazione su rivista::01a Articolo in rivista
A note on convergence of level sets / Camilli, Fabio. - In: ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN. - ISSN 0232-2064. - STAMPA. - 18:(1999), pp. 3-12.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/405738
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