Generalized Cotorsion Locally Compact abelian Groups
We prove a Lyapunov type theorem for modular measures on lattice ordered effect algebras.
We extend a result of Rangaswamy about regularity of endomorphism rings of Abelian groups to arbitrary topological Abelian groups. Regularity of discrete quasi-injective modules over compact rings modulo radical is proved. A characterization of torsion LCA groups for which is regular is given.
Consider the four pairs of groups , , and , where , are locally compact second countable abelian groups, is a dense subgroup of with inclusion map from to continuous; is a closed subgroup of ; , are the duals of and respectively, and is the annihilator of in . Let the first co-ordinate of each pair act on the second by translation. We connect, by a commutative diagram, the systems of imprimitivity which arise in a natural fashion on each pair, starting with a system...
Soit un groupe localement compact abélien ou un groupe de Lie et un compact parfait de . Il existe alors un compact de mesure de Haar nulle tel que soit d’intérieur non vide. En particulier si est métrisable, les seuls ensembles analytiques tels que soit de mesure nulle dès que l’est, sont dénombrables.