A Criterion for Precompactness in the Space of Hypermeasures
| dc.creator | Yurachkivsky, Andriy | |
| dc.date | 2007-09-19 | |
| dc.date.accessioned | 2026-07-07T08:30:51Z | |
| dc.date.available | 2026-07-07T08:30:51Z | |
| dc.description | Let $Q$ denote the space of signed measures on the Borel $σ$-algebra of a separable complete space $X$. We endow $Q$ with the norm $\|q\|=\sup|\intϕdq|$, where the supremum is taken over all Lipschitz with constant 1 functions whose module does not exceed unity. This normed space is incomplete provided $X$ is infinite and has at least one limit point. We call its completion the space of hypermeasures. Necessary and sufficient conditions for precompactness (=relative compactness) of a set of hypermeasures are found. They are similar to those of Prokhorov's and Fernique's theorems for measures. | |
| dc.description | 6 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/0709.2999 | |
| dc.identifier | http://arxiv.org/abs/0709.2999 | |
| dc.identifier | Dopovidi Natsionalnoi Akademii Nauk Ukrainy [Reports Nat. Acad. Sci. Ukr.], 2006, No.9, p.38-41 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138347 | |
| dc.subject | Functional Analysis | |
| dc.subject | 28C05 | |
| dc.title | A Criterion for Precompactness in the Space of Hypermeasures | |
| dc.type | text |