2015/11/17 by Panu Lahti, Lahti, Panu, Nageswari Shanmugalingam +1 · 3 citations
Mathematics · #26B30 #30L99 #43A85 #Advanced Topology and Set Theory #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Dynamics and Fractals #math.AP #msc:26B30 #msc:30L99 #msc:43A85
paper · pdf · doi:10.48550/arxiv.1511.05504
arxiv created 2015/11/17 · openalex publication_date 2015/11/17 · arxiv updated 2015/11/18 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
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 ``one-sidedly" 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.