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On Extensions of Monotone Functions from Linear SubLattices

Published online by Cambridge University Press:  20 November 2018

H. W. Ellis
H. W. Ellis*
Affiliation:
Summer Research Institute, Queen's University Kingston
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In this note real valued functions, defined on a linear sublattice S of a linear lattice R and satisfying the two order conditions (M1) and (M2), are studied from the point of view of the existence and uniqueness of extensions to R. The paper is partly expository and supplements and extends §3 of [4] where S was assumed to be an ℓ-ideal.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 3 , April 1965 , pp. 329 - 343
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Birkhoff, G., Lattice Theory, American Mathematical Society Colloquium Publications, Vol. XXV, New York, 1948.Google Scholar
2. Bourbaki, N., Éléments de Mathématique, Fasc. XIII, "Intégration", Chaps. I-IV (Paris, 1952).Google Scholar
3. Ellis, H.W. and Halperin, I., Function Spaces determined by a levelling length function, Can. J. Math., 5(1953), 576-592.CrossRefGoogle Scholar
4. Ellis, H.W. and Nakano, Hidegorô, "Monotone functions on linear lattices", Can. J. Math., 15 (1963), 226-236.CrossRefGoogle Scholar