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{\bf  PROBLEM SET 2b}
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\begin{enumerate}

\item Suppose $\{f_n\}$ is a sequence of continuous functions and let
       $E$ be the set of $x$'s where the seqeunce converges. Show
      that $E$ is Borel, and hence Lebesgue measurable.

\item Is the set of rational numbers equal to the intersection of some 
      countable collection of open sets?

\item  Must the continuous image of a measurable set be measureable?

\end{enumerate}

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