2007/11/15 by Jinshan Zhang, Zhang, Jinshan
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #Rings, Modules, and Algebras #math.GM #math.PR #msc:03E20 #msc:31C99
paper · pdf · doi:10.48550/arxiv.0711.2400
8 pages
arxiv created 2008/12/11 · arxiv updated 2009/12/01
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.