→ ppia :Q2用對角線法 同Baby Rudin證A-A thm.的方法 07/27 18:18
Q1. Let E_n be Lebesgue measurable subsets of [0,1] and m(E_n)→1, where m is
the Lebesgue measure. Show that there is a subsequence {E_(n_j)} so that
∞
m( ∩ E ) > 0.
j=1 n_j
Q2. Let f_n:E→R so that f_n→f pointwise on E, where E is an uncountable set.
Prove that there is an infinite subset A of E so that f_n→f uniformly on A.
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