Question: 4. For an integrable random variable , we have by dominated convergence that limrE[;>r]=E[limr1{>r}]=E[0]=0. For a family of random variables {t;tT}, we call it uniformly

4. For an integrable random variable , we have by dominated

convergence that limrE[;>r]=E[limr1{>r}]=E[0]=0. For a family of random variables {t;tT}, we call

4. For an integrable random variable , we have by dominated convergence that limrE[;>r]=E[limr1{>r}]=E[0]=0. For a family of random variables {t;tT}, we call it uniformly integrable if limrsuptTE[t;t>r]=0 Prove that (b) if there exists a function G:R+R+which is increasing and such that G(x)/x as x and suptTE[G(t)]r]=E[limr1{>r}]=E[0]=0. For a family of random variables {t;tT}, we call it uniformly integrable if limrsuptTE[t;t>r]=0 Prove that (b) if there exists a function G:R+R+which is increasing and such that G(x)/x as x and suptTE[G(t)]

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