Partial Densities on Locally Compact Abelian Groups and Uniformly Distributed Sequences

Niederreiter, Harald; Sookoo, Norris

doi:10.1007/s00605-001-0472-x

Cited by 2 publications

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“…Maharam [5] studied a family of measures with orthogonality properties and Schmidt [8] proved that a particular ordered Banach space of vector measures is a Banach lattice. Systems of measures satisfying compatibility conditions were studied by Niederreiter and Sookoo [6,7] , who obtained conditions under which a partial density can be extended to a density. Sookoo and Chami [9] investigated the lattice structure of certain sets of lattices of measures defined on the quotient spaces of the integers.…”

Section: Introductionmentioning

confidence: 99%

Homomorphisms on Lattices of Measures

Sookoo¹,

Chami²

2009

J. of Mathematics and Statistics

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Problem statement: Homomorphisms on lattices of measures defined on the quotient spaces of the integers were considered. These measures were defined in terms of Sharma-Kaushik partitions. The homomorphisms were studied in terms of their relationship with the underlying Sharma-Kaushik partitions. Approach: We defined certain mappings between lattices of Sharma-Kaushik partitions and showed that they are homomorphisms. These homomorphisms were mirrored in homorphisms between related lattices of measures. Results: We obtained the structure of certain homomorphisms of measures. Conclusion: Further information about homomorphisms between lattices of measures of the type considered here can be obtained by investigating the underlying lattices of Sharma-Kaushik partitions

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