Zeitschrift für Analysis und ihre Anwendungen
Vol. 18, No. 1, pp. 3-12 (1999)
A Note on Convergence of Level Sets
F. CamilliUniv. dell` Aquila, Dip. di Energetica, 67040 Roio Poggio (AQ), Italy, e-mail: firstname.lastname@example.org
Abstract: 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
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Electronic fulltext finalized on: 25 Apr 2000. This page was last modified: 9 Nov 2001.