Let En, n = 1, 2,... be a sequence of measurable subsets of R. (a) If En ≤ En+1 for n = 1, 2, then show that m(Ux=1 En) = = lim m(En). n→∞ (b) If En+1 ≤ En for n = 1,2,.. and m(E₁) < ∞ then show that m(En) = lim m(En). n→∞ Further construct an example to show that this may fail if m(E₁) : = ∞ (the condition is necessary).

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