\documentclass[12pt]{article}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{fullpage,amsmath,amssymb,amsthm,framed,graphicx,color}
\newtheorem{theorem}{Theorem}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{lemma}[theorem]{Lemma}
\usepackage{pifont}% http://ctan.org/pkg/pifont
\newcommand{\cmark}{\ding{51}}%
\newcommand{\xmark}{\ding{55}}%

\def\NN{\mathbb{N}}
\def\ZZ{\mathbb{Z}}
\def\RR{\mathbb{R}}
\def\QQ{\mathbb{Q}}
\def\CC{\mathbb{C}}
\def\KK{\mathbb{K}}

\def\cO{\mathcal{O}}
\def\cP{\mathcal{P}}
\def\cA{\mathcal{A}}
\def\cB{\mathcal{B}}
\def\cC{\mathcal{C}}
\def\cF{\mathcal{F}}
\def\cH{\mathcal{H}}
\def\cR{\mathcal{R}}
\def\cN{\mathcal{N}}
\def\cL{\mathcal{L}}

\def\ee{\varepsilon}
\def\ii{\mathfrak{i}}

\newcommand{\mb}[1]{\ensuremath{\mathbf{ #1 }}}
\newcommand{\norm}[1]{\ensuremath{\left\| #1\right\| }}
\newcommand{\enorm}[1]{\ensuremath{|\!|\!| #1|\!|\!| }}

\DeclareMathOperator*{\esssup}{ess\,sup}
\DeclareMathOperator*{\supp}{supp}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\noindent
\rule{\textwidth}{0.05cm}
\begin{center}
{{\Large\bf Section 2.6:} \bf 2 (optional)}
\end{center}
\rule[0.2cm]{\textwidth}{0.05cm}

\begin{enumerate}

\item[2.] \textbf{(Optional)} Let $1\leq p<\infty$, and let $f_n\in L^p(\Omega)$ for
  $n\geq 1$, and $f\in L^p(\Omega)$.  Suppose that $f_n\to f$
  pointwise almost everywhere, and $\|f_n\|_{L^p(\Omega)}\to
  \|f\|_{L^p(\Omega)}$ , as $n\to\infty$.  Show that
  $\|f_n-f\|_{L^p(\Omega)}\to 0$ as $n\to\infty$.
    
\end{enumerate}


\end{document}