Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


An additive representation for real functions on the product of a set and a lattice

Author: W. J. R. Eplett
Journal: Proc. Amer. Math. Soc. 81 (1981), 23-26
MSC: Primary 06A15
MathSciNet review: 589130
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Given a real-valued function defined on the product of an arbitrary set and a finite lattice, a necessary and sufficient condition is obtained for the existence of an additive representation for the function in terms of functions on sublattices of the original lattice. This additive representation is of the nature of a recurrence and provides a tool for further analysis of the function. An example is given for a case where the lattice concerned is the lattice of partitions of a finite set. The main theorem of this paper generalizes a result due to Fishburn corresponding to the lattice being the lattice of subsets of a finite set.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 06A15

Retrieve articles in all journals with MSC: 06A15

Additional Information

PII: S 0002-9939(1981)0589130-X
Article copyright: © Copyright 1981 American Mathematical Society