SOME ASPECTS OF THE LIFTING PROPERTY OF THE SPACE #xA3;#x221E;(#x3BC;,X)

摘要

Using a lifting of #xA3;#x221E;(#x3BC;,X) (5,6), we construct a lifting #x3C1;xof the seminormed vector space #xA3;#x221E;(#x3BC;,X) of measurable, essentially boundedX-valued functions. We show that in a certain sense such a lifting always exists. If #x3BC; is Lebesgue measure on (0, 1) we show that #x3C1;xexists as map from #xA3;#x221E;((O, 1),X) #x2192; #xA3;#x221E;,((0, l),X) if and only if X is reflexive. In general the lifted function takes its values inX**. Therefore we investigate the question, when f #x3B5; #xA3;#x221E;(#x3BC;,X) is strictly liftable in the sense that the lifted function is a map with values even inX.