Abstract
We develop a capacity theory based on the definition of Sobolev functions on metric spaces with a Borel regular outer measure. Basic properties of capacity, including monotonicity, countable subadditivity and several convergence results, are studied. As an application we prove that each Sobolev function has a quasicontinuous representative. For doubling measures we provide sharp estimates for the capacity of balls. Capacity and Hausdorff measures are related under an additional regularity assumption on the measure.
Original language | English |
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Pages (from-to) | 367-382 |
Number of pages | 16 |
Journal | ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA |
Volume | 21 |
Issue number | 2 |
Publication status | Published - 1996 |
MoE publication type | A1 Journal article-refereed |