Zeitschrift für Analysis und ihre Anwendungen Vol. 18, No. 1, pp. 312 (1999) 

A Note on Convergence of Level SetsF. CamilliUniv. dell` Aquila, Dip. di Energetica, 67040 Roio Poggio (AQ), Italy, email: camilli@ing.univaq.itAbstract: Given a sequence of functions $f_n$ converging in some topology to a function $f$, in general the $0$level set of $f_n$ 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 $f_n$, 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 $f_n$ to $f$. Keywords: perturbed level sets, set convergence, capacity Classification (MSC2000): 28A12, 46E35 Full text of the article:
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