Measures on the Quotient Spaces of the Integers

Abstract

SK-partitions were introduced by Sharma and Kaushik, who defined distances (metrics) between vectors in terms of partitions of the alphabet set F_q , the set of the ring of integers modulo q. These distances were applied in Coding Theory. The research examined algebraic and topological aspects of SK-partitions and related sets of measures. A lattice of SK-partitions was introduced and shown to have distributive sub lattices. Generator sets of the lattice were obtained and the structure of its ideals and filters examined. Corresponding results for lattices of measures were presented.