Remarks on ranges of charges on $\sigma$-fields
Rao, K. P. S. Bhaskara
Illinois J. Math., Tome 28 (1984) no. 4, p. 646-653 / Harvested from Project Euclid
In this paper we present the following results about ranges of charges on a $\sigma$-field $\mathcal{A}$ of subsets of a set $X$. [start-list] *(1) For any bounded charge the range is either a finite set or contains a perfect set, contrary to an assertion made by Sobezyk and Hammer [8]. *(2) If $\mu_{1},\mu_{2},\ldots,\mu_{n}$ are strongly continuous bounded charges on $\mathcal{A}$ then the range of the vector measure $(\mu_{1},\mu_{2},\ldots,\mu_{n})$ is a convex set and need not be closed. *(3) There is a positive bounded charge, on any infinite $\sigma$-field, whose range is neither Lebesgue measurable nor has the property of Baire.[end-list]
Publié le : 1984-12-15
Classification:  28A99,  28A60
@article{1256045971,
     author = {Rao, K. P. S. Bhaskara},
     title = {Remarks on ranges of charges on $\sigma$-fields},
     journal = {Illinois J. Math.},
     volume = {28},
     number = {4},
     year = {1984},
     pages = { 646-653},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1256045971}
}
Rao, K. P. S. Bhaskara. Remarks on ranges of charges on $\sigma$-fields. Illinois J. Math., Tome 28 (1984) no. 4, pp.  646-653. http://gdmltest.u-ga.fr/item/1256045971/