Capacity functor in the category of compacta

Наближення Ємностей На Метричних Просторах Ліпшицевими Ємностями

“…Надалi розглядаємо клас ємностей [2] на просторi (X, d), регулярних щодо метрики d, тобто таких монотонно неспадних дiйснозначних функцiй c на сукупностi Exp X всiх замкнених пiдмножин простору X, що c(…”

Continuous approximations of capacities on metric compacta

“…It was shown in [2] that MX carries a compact Hausdorff topology with the subbase of all sets of the form…”

“…We follow the terminology and notation of [2] and denote by exp X the set of all non-empty closed subsets of a compactum X. The set exp X is considered with the Vietoris topology.…”

“…Thus (MX, ∨, ∧) is a (left idempotent) (I, max, min)-semimodule. Recall (see [2]) that the subbase of all sets of the form O − (F, a) and…”

“…Spaces of upper semicontinuous capacities on compacta were systematically studied in [2]. In particular, in the latter paper functoriality of the construction of a space of capacities was proved and Prokhorov-style and Kantorovich-Rubinstein-style metrics on the set of capacities on a metric compactum were introduced.…”