Question: 1.10. Suppose that for a < b, we have /J>{Xn < a i.o. and X/1 > b i.o.} = 0; 80 I CONVERGENCE CONCEPTS then

1.10. Suppose that for a <

b, we have

/J>{Xn < a i.o. and X/1 > b i.o.} = 0;

80 I CONVERGENCE CONCEPTS then limll ...... oc XIl exists a.e. but it may be infinite. [HINT: Consider all pairs of rational numbers

(a.

b) and take a union over them.]

Under the assumption of independence, Theorem 4.2.1 has a striking complement.

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