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In the present paper we study majorizable operators acting onBanach-Kantorovich $L_p$-lattices, constructed by a measure $m$ with values inthe ring of all measurable functions. Then using methods of measurable bundlesof Banach-Kantorovich lattices, we prove the strong "zero-two" law for positivecontractions of the Banach-Kantorovich $L_p$-lattices.

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