# A Note on Convergence of Level Sets

### Fabio Camilli

Università di Roma La Sapienza, Italy

## 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 $g$. 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 $f$.

## Cite this article

Fabio Camilli, A Note on Convergence of Level Sets. Z. Anal. Anwend. 18 (1999), no. 1, pp. 3–12

DOI 10.4171/ZAA/865