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.
|Number of pages||16|
|Journal||ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA|
|Publication status||Published - 1996|
|MoE publication type||A1 Journal article-refereed|