
Accession Number : AD0288009
Title : A CONTRIBUTION TO THE ASYMPTOTIC ANALYSIS IN LATTICEORDERED 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 realvalued and continuous function defined on R . It is wellknown 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 MooreSmith definition of convergence. (Author)
Descriptors : *ALGEBRA, *FUNCTIONAL ANALYSIS, FUNCTIONS(MATHEMATICS), REAL VARIABLES
Distribution Statement : APPROVED FOR PUBLIC RELEASE