This exercise, and the two following, will look at some of the mathematical details of convergence (a) Prove Theorem 5 5 4 (Hint Since h is continuous, given 0 we can find a S such that h(xn) h(x) whenever xn x Translate this into probability statements ) (b) In Example 5 5 8, find a subsequence of the XiS that converges almost surely, that is, that converges pointwise

Question: This exercise, and the two following, will look at some of the mathematical details of convergence. (a) Prove Theorem 5.5.4. (Hint: Since h is continuous,

This exercise, and the two following, will look at some of the mathematical details of convergence.
(a) Prove Theorem 5.5.4. (Hint: Since h is continuous, given ∈ > 0 we can find a S such that |h(xn) - h(x)\< ∈ whenever |xn - x| < δ. Translate this into probability statements.)
(b) In Example 5.5.8, find a subsequence of the XiS that converges almost surely, that is, that converges pointwise.

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