Proper 1-ball contractive retractions in spaces of measurable functions

n this paper we consider the Wo´sko problem ([20]) of evaluating, in aninfinite-dimensional Banach space X, the infimum of all k \ge 1 for which thereexists a k-ball contractive retraction of the unit ball onto its boundary. Weprove that in some classical Banach spaces the best possible value 1 is attained.Moreover we give estimates of the lower H-measure of noncompactness of theretractions we construct.