A CONTRIBUTION TO THE ASYMPTOTIC ANALYSIS IN LATTICE-ORDERED GROUPS
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1962
- Accession Number
- AD0288009
Entities
People
- J. Karamata
- M. Vuilleumier
- R. Bojanic
Organizations
- University of Wisconsin–Madison