Hüsseinov, F.2016-02-082016-02-0820090165-4896http://hdl.handle.net/11693/22812A simple proof of the equivalence of Pareto optimality plus positiveness and α-maxmin optimality, dispensing with the assumption of closedness of the utility possibility set, is given. Also the structure of the set of Pareto optimal utility profiles is studied. © 2008 Elsevier B.V. All rights reserved.Englishα-equitabilityα-maxmin optimalityFair divisionNon-atomic probability spacePareto optimalityα-maxmin solutions to fair division problems and the structure of the set of Pareto utility profilesArticle10.1016/j.mathsocsci.2008.11.003