Geodesic
On vector lattices of elementary Carathéodory functions
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 1, pp. 223-236.

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In this paper we deal with the vector lattice $C(B)$ of all elementary Carathéodory functions corresponding to a generalized Boolean algebra $B$.
Classification : 06F20, 46A40
Keywords: generalized Boolean algebra; elementary Carathéodory functions; Specker lattice ordered group; $(\alpha, \beta)$-distributivity; complete distributivity 
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Jakubík, Ján. On vector lattices of elementary Carathéodory functions. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 1, pp. 223-236. http://geodesic.mathdoc.fr/item/CMJ_2005__55_1_a16/