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.File allegati a questo prodotto
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