Maharam extensions of positive operators and \(f\)-modules (Q1611288)

Among other things, it is proved that, for suitable extensions of collections of positive order-continuous linear functionals on vector lattices, the assertion of the Radon-Nikodym theorem is true. The main result of the paper provides a way to construct a simultaneous extension of collections of positive linear operators between Archimedean Riesz spaces to Maharam (i.e., interval-preserving) operators between certain Dedekind complete Riesz spaces. The technique of construction of such extensions is based upon properties of the so-called \(f\)-modules.