Question: 1.7. We have SII/n ~ 0 a.e. if and only if the following two conditions are satisfied: (i) Sn/n ~ a in pr., (ii) S

1.7. We have SII/n ~ 0 a.e. if and only if the following two conditions are satisfied:

(i) Sn/n ~ a in pr.,

(ii) S 2" 12n ~ 0 a.e.;

an alternative set of conditions is (i) and

(iii) 'VE > 0: LII ?J>(IS2"+' -S2"! > 21lE) < 00.

{S I }. . fonnly integrable and

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