Geodesic
Properties of capacities generated by Sobolev classes on metric measure spaces
Trudy Instituta matematiki, Tome 24 (2016) no. 2, pp. 20-31

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Properties of $\mathrm{Cap}_{\alpha, p}$–capacities, generated by Sobolev classes on metric spaces with doubling measure, are investigated. The principal case is $p>0$ not investigated before. It's proved that capacity is an outer measure; the property of continuity, the relation between different capacities, measure and Hausdorff dimension is investigated. 
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     author = {S. A. Bondarev},
     title = {Properties of capacities generated by {Sobolev} classes on metric measure spaces},
     journal = {Trudy Instituta matematiki},
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     url = {http://geodesic.mathdoc.fr/item/TIMB_2016_24_2_a2/}
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S. A. Bondarev. Properties of capacities generated by Sobolev classes on metric measure spaces. Trudy Instituta matematiki, Tome 24 (2016) no. 2, pp. 20-31. http://geodesic.mathdoc.fr/item/TIMB_2016_24_2_a2/