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Zeitschrift für Analysis und ihre Anwendungen


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Volume 18, Issue 1, 1999, pp. 3–12
DOI: 10.4171/ZAA/865

Published online: 1999-03-31

A Note on Convergence of Level Sets

Fabio Camilli[1]

(1) Università di Roma La Sapienza, Italy

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 $g$. 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

Camilli Fabio: A Note on Convergence of Level Sets. Z. Anal. Anwend. 18 (1999), 3-12. doi: 10.4171/ZAA/865