Geodesic
On Extensions of Monotone Functions from Linear SubLattices
Canadian mathematical bulletin, Tome 8 (1965) no. 3, pp. 329-343

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Ellis, H. W. On Extensions of Monotone Functions from Linear SubLattices. Canadian mathematical bulletin, Tome 8 (1965) no. 3, pp. 329-343. doi: 10.4153/CMB-1965-024-6
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[1] 1. Birkhoff, G., Lattice Theory, American Mathematical Society Colloquium Publications, Vol. XXV, New York, 1948. Google Scholar

[2] 2. Bourbaki, N., Éléments de Mathématique, Fasc. XIII, "Intégration", Chaps. I-IV (Paris, 1952). Google Scholar

[3] 3. Ellis, H.W. and Halperin, I., Function Spaces determined by a levelling length function, Can. J. Math., 5(1953), 576-592. Google Scholar | DOI

[4] 4. Ellis, H.W. and Nakano, Hidegorô, "Monotone functions on linear lattices", Can. J. Math., 15 (1963), 226-236. Google Scholar | DOI

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