@article{Cherkovskyi_2014, title={Regular capacities on metrizable spaces}, volume={6}, url={https://scijournals.pnu.edu.ua/index.php/cmp/article/view/1348}, DOI={10.15330/cmp.6.1.166-176}, abstractNote={It is proved that for a (not necessarily compact) metric space: the metrics on the space of capacities in the sense of Zarichnyi and Prokhorov are equal; completeness of the space of capacities is equivalent to completeness of the original space. It is shown that for the capacities on metrizable spaces the properties of $\omega$-smoothness and of $\tau$-smoothness are equivalent precisely on the separable spaces, and the properties of $\omega$-smoothness and of regularity w.r.t. some (then w.r.t. any) admissible metric are equivalent precisely on the compact spaces.}, number={1}, journal={Carpathian Mathematical Publications}, author={CherkovskyiT.M.}, year={2014}, month={Jul.}, pages={166-176} }