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

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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. 
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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     author = {Ellis, H. W.},
     title = {On {Extensions} of {Monotone} {Functions} from {Linear} {SubLattices}},
     journal = {Canadian mathematical bulletin},
     pages = {329--343},
     year = {1965},
     volume = {8},
     number = {3},
     doi = {10.4153/CMB-1965-024-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1965-024-6/}
}
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