Fine properties and a notion of quasicontinuity for BV functions on metric spaces
Abstract
On a metric space equipped with a doubling measure supporting a Poincaré inequality, we show that given a BV function, discarding a set of small $1$capacity makes the function continuous outside its jump set and ``onesidedly" continuous in its jump set. We show that such a property implies, in particular, that the measure theoretic boundary of a set of finite perimeter separates the measure theoretic interior of the set from its measure theoretic exterior, both in the sense of the subspace topology outside sets of small $1$capacity, and in the sense of $1$almost every curve.
 Publication:

arXiv eprints
 Pub Date:
 November 2015
 arXiv:
 arXiv:1511.05504
 Bibcode:
 2015arXiv151105504L
 Keywords:

 Mathematics  Analysis of PDEs;
 30L99;
 26B30;
 43A85