The “zero-two” law in Orlicz–Kantorovich spaces

The present paper deals with \(L_0\)-valued measures and the associated Orlicz–Kantorovich lattice. The considered Orlicz–Kantorovich lattice, endowed with the Luxemburg norm, is represented as a measurable bundle of classical Orlicz spaces associated with scalar measures. This kind of representation allows us to investigate positive contractions and apply the corresponding zero-two laws on the classical Orlicz spaces, to prove vector versions of “zero-two” laws on the considered Orlicz–Kantorovich space.