On the punctual and local ergodic theorem for nonpositive power bounded operators in ^{}_{}[0,1],1<<+∞

We show in this note that there exists a function / e fit 0) of power bounded operators in each Lp (1 Lp(il, se, P) satisfies the punctual ergodic theorem (p.e.t.) if for each/g Lp(ti,se,P)