Constituting Atoms of a $σ$ Algebra via Its Generator
| dc.creator | Zhang, Jinshan | |
| dc.date | 2007-11-15 | |
| dc.date | 2008-12-11 | |
| dc.date.accessioned | 2026-07-07T12:11:31Z | |
| dc.date.available | 2026-07-07T12:11:31Z | |
| dc.description | To constitute atoms of a $σ$ algebra is not a easy task due to the large number of its elements. However, determining them via generators seems a feasible and simple way since most $σ$ algebras are generated by their smaller proper subsets. Precisely, under some conditions each atom of a $σ$ algebra equals the intersection of the elements containing a point of the atom in the generator. In this paper, a very weak sufficient condition for determining atoms by the generator is presented. The condition, though not being a necessary one, is shown to be almost the weakest one in the sense that it can hardly be improved. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/0711.2400 | |
| dc.identifier | http://arxiv.org/abs/0711.2400 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/210239 | |
| dc.subject | Probability | |
| dc.subject | General Mathematics | |
| dc.subject | 03E20, 31C99 | |
| dc.title | Constituting Atoms of a $σ$ Algebra via Its Generator | |
| dc.type | text |