Bourgain, J. Israel J. Math. (1980) 37: 34. doi:10.1007/BF02762866
Using the duality between Dunford-Pettis operators onL1 and Pettis-Cauchy martingales, we prove that the Dunford-Pettis operators fromL1 intoL1 form a lattice. We show also that a Banach spaceX has the Radon-Nikodým property provided the Dunford-Pettis members of ℒ(L1,X) are representable. The lifting of dual valued Dunford-Pettis operators is investigated. Some remarks are included.