that $L_p$-spaces associated with central-valued traces are Banach-Kantorovich spaces. The theory of Banach-Kantorovich spaces is now sufficiently well-developed (for instance, see [@Kus; @K2]). The methods of Boolean valued analysis play an important role in the theory. Using these methods, the Banach-Kantorovich lattices and the corresponding homomorphisms can be interpreted as the Banach lattice and bounded linear operators within a suitable Boolean valued model of set theory [@Kus]. This approach to the theory of Banach-Kantorovich lattices makes ut possible to use the transfer principle [@Kus] for obtaining various properties of Banach-Kantorovich lattices that are analogous of the corresponding properties of classical Banach lattices. Naturally, when using such a method, an additional study is needed for establishing the required interrelation between the objects of 2-valued and Boolean valued models of set theory.

Another important approach to study Banach-Kantorovich spaces is provided by the theory of continuous and measurable Banach bundles [@G0]-[@G2]. In this approach the representation of a Banach-Kantorovich lattice as a space of measurable sections of a measurable Banach bundle makes it possible to obtain the needed properties of the lattice by means of the corresponding stalkwise verification of the properties. As an application of this approach, in [@Ga] it has 