TY - JOUR
AU - Cherkovskyi, T.M.
PY - 2014/07/15
Y2 - 2023/12/11
TI - Regular capacities on metrizable spaces
JF - Carpathian Mathematical Publications
JA - Carpathian Math. Publ.
VL - 6
IS - 1
SE - Scientific articles
DO - 10.15330/cmp.6.1.166-176
UR - https://scijournals.pnu.edu.ua/index.php/cmp/article/view/1348
SP - 166-176
AB - 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.
ER -