Accession Number : AD0288009

Title :   A CONTRIBUTION TO THE ASYMPTOTIC ANALYSIS IN LATTICE-ORDERED GROUPS

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : BOJANIC,R. ; KARAMATA,J. ; VUILLEUMIER,M.

Report Date : SEP 1962

Pagination or Media Count : 1

Abstract : Let f(x) be a real-valued and continuous function defined on R . It is well-known that if, for every fixed t , lim f(x + t) - f(x) = O , as x approaches infinity, then the convergence is uniform for t in any closed interval. The statement still holds for functions of several variables, i.e., in the ordered real space R to the nth power with the Pringsheim definition of convergence. One can show this by considering real valued functions defined on a latticeordered group. It is then possible to obtain some extension of this result if one requires that the lattice satisfies some appropriate conditions and if one takes the Moore-Smith definition of convergence. (Author)

Descriptors :   *ALGEBRA, *FUNCTIONAL ANALYSIS, FUNCTIONS(MATHEMATICS), REAL VARIABLES

Distribution Statement : APPROVED FOR PUBLIC RELEASE