The strong ``zero-two" law for positive contractions of Banach--Kantorovich Lₚ-lattices

In the present paper we study dominated operators acting on Banach--Kantorovich Lₚ-lattices, constructed by a measure m with values in the ring of all measurable functions. Using methods of measurable bundles of Banach--Kantorovich lattices, we prove the strong ``zero-two" law for positive contractions of Banach--Kantorovich Lₚ-lattices. \{1mm}