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We show that the minimal hull of a convex set in a Banach space is not necessarily convex, even in / spaces (finite-or infinite-dimensional). This answers a question raised by B. Beauzamy and B. Maurey in their joint paper of 1977. We also carry out a careful study of the minimal hull and the saturation of the unit ball in /j . Finally, we give a compactness theorem for the minimal hull in /. .doi:10.2307/2047872 fatcat:wd447fqwjjegxfxbgyff5el7nm