Norris Sookoo
University of the West Indies, St. Augustine Trinidad, West Indies
Ashok Sahai
University of the West Indies, St. Augustine Trinidad, West Indies
ABSTRACT
Conditions are obtained under which a partial density on a certain class of locally compact abelian groups can be extended to a density. These groups each consist of the integral multiples of a particular rational number, with the discrete topology. It is established that a collection of compatible measures on some of the quotient groups of one such group can be induced by a measure on a particular quotient group. This leads to the result that a partial density can be extended to a density when compatibility conditions are satisfied.
PDF References Citation
How to cite this article
Norris Sookoo and Ashok Sahai, 2007. Partial Densities on the Rational Numbers. Journal of Applied Sciences, 7: 830-834.
DOI: 10.3923/jas.2007.830.834
URL: https://scialert.net/abstract/?doi=jas.2007.830.834
DOI: 10.3923/jas.2007.830.834
URL: https://scialert.net/abstract/?doi=jas.2007.830.834
REFERENCES
- Carnal, H. and G.M. Feldman, 1995. Phase retrieval for probability measures on abelian groups. J. Theor. Probability, 8: 717-725.
Direct Link - Carnal, H. and G.M. Feldman, 1997. Phase retrieval for probability measures on abelian groups II. J. Theor. Probability, 10: 1065-1074.
Direct Link - Carnal, H. and G.M. Feldman, 2000. A stability property for probability measures on abelian groups. Stat. Probability Lett., 49: 39-44.
Direct Link - Del Muto, M. and A. Figa-Talamanca, 2006. Anisotropic diffusion on totally disconnected abelian groups. Pac. J. Math., 225: 221-230.
Direct Link - Niederreiter, H. and N. Sookoo, 2000. Partial densities on the group of integers. Arch. Math., 36: 17-24.
Direct Link - Niederreiter, H. and N. Sookoo, 2002. Partial densities on locally compact abelian groups and uniformly distributed sequences. Monatsh Math., 136: 243-247.
Direct Link