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A new characterization of Clarke's normal cone to a closed set in a Banach space is given. The normal cone is characterized in terms of weak-star limits of epsilon normals. A similar characterization of Clarke's generalized gradients is also presented. Restrictions must be placed on the Banach spaces to make the formulas valid.doi:10.1090/s0002-9947-1986-0819935-8 fatcat:wdwxrsrr7zaexpcn5hucjgpuma