Fine properties and a notion of quasicontinuity for BV functions on metric spaces.(English. French summary)Zbl 1359.30055
Summary: 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.
MSC:
| 30L99 | Analysis on metric spaces |
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References:
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