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. 223–225DOI 10.4171/RLM/465