Local clustering of the non-zero set of functions in

  • Emmanuele DiBenedetto

    Vanderbilt University, Nashville, United States
  • Ugo Gianazza

    Università di Pavia, Italy
  • Vincenzo Vespri

    Universita di Firenze, Italy

Abstract

We extend to the case a measure theoretic result previously proved by DiBenedetto and Vespri for functions that belong to where is a -dimensional cube of edge centered at . It basically states that if the set where is bounded away from zero occupies a sizable portion of , then the set where is positive clusters about at least one point of .

Cite this article

Emmanuele DiBenedetto, Ugo Gianazza, Vincenzo Vespri, Local clustering of the non-zero set of functions in . Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 17 (2006), no. 3, pp. 223–225

DOI 10.4171/RLM/465