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llx~yll~ + HyxW,l~# < i/n 6 n(x) x6M e for p(n) > n of e w e Wn(X) For n>l choose (5) p(n) e Wn(X), (6) llxP(n)y p(n) - (xy)p(n) II~ < I/n , (7) ll[xp(n), an]II~ < I/n (8) I~(anx p(n)) - ~ ( a n T e ( x ) ) I < I/n , x ~ N n, a e F n, (9) IiB(xp(n)) - (8e(x))P(n)II~ < i/n , x eNn, 8 E Aut M • and xeN.

K N [33] to g,h • G. ~ • ~/~. which is semiliftable state on G (Nonabelian Rohlin Theorem). able amenable predual, (not n e c e s s a r i l y but for a m e n a b l e groups this p r o b l e m is still open. Recall that a crossed action of ~I = 1 For free actions the t h e o r e m of Connes was e x t e n d e d in a b e ! i a n groups, If ([4]). }[ " f o r g,i,j,k,£ ; all (Ei,k)i, k can be chosen g,h,i,k . in the relative commutant in M~ 42 o f any given countable The estimate subset Me . (i) above is an average estimate.

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