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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An additive representation for real functions on the product of a set and a lattice
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by W. J. R. Eplett PDF
Proc. Amer. Math. Soc. 81 (1981), 23-26 Request permission

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.
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 81 (1981), 23-26
  • MSC: Primary 06A15
  • DOI: https://doi.org/10.1090/S0002-9939-1981-0589130-X
  • MathSciNet review: 589130