A notion of fine continuity for BV functions on metric spaces

Abstract

In the setting of a metric space equipped with a doubling measure supporting a Poincaré inequality, we show that BV functions are, in the sense of multiple limits, continuous with respect to a 1-fine topology, at almost every point with respect to the codimension 1 Hausdorff measure.

arXiv commentarXiv admin note: text overlap with arXiv:1511.05504