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\begin{center}\textbf{Problem Set 9 \hspace{.7in} Real Analysis 1 \hspace{.7in} Due 11/24/14} \end{center}

\noindent Four of these problems will be graded, with each problem worth 5 points.  Clear and complete justification is required for full credit.  You are welcome to discuss these problems with anyone and everyone, but must write up your own final submission without reference to any sources other than the textbook and instructor. 

\begin{enumerate}
\item Prove Lemma 6.1.3.
\item Prove that $U(\mathscr{Q} , f ) \leq U( \mathscr{P}, f )$ in Lemma 6.1.5.
\item Do Exercise 6.1.3.
\item  Do Exercise 6.1.4.
\item Do Exercise 6.1.6.
\item Do Exercise 6.2.5.
\item Do Exercise 6.2.11.
\item Do Exercise 6.3.1.

\end{enumerate}

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