Question: If for n = 1, 2,..., the r.v.s {Xn} and {Yn} are uniformly integrable, show that {Xn + Yn} are also uniformly integrable?

If for n = 1, 2,..., the r.v.s {Xn} and {Yn} are uniformly integrable, show that {Xn + Yn} are also uniformly integrable?

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