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\lecture{12}{May 26, 2008}{Guy Kindler}{Ori Gurel-Gurevich}
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So far, we used elementary techniques. Today we will do something
less elementary, for the first time.
\section*{Reminders and Preliminaries}
\begin{definition}
The \emph{$L_p$-norm} of a function $f:\{\pm 1\}^n\rightarrow \R$ is
$$\|f\|_p=(\E[|f(x)|^p])^{1/p}$$
for $1\le p < \infty$ and
$$\|f\|_\infty=\max_{x\in \{\pm 1\}^n} |f(x)|$$
\end{definition}
\noindent We already proved \emph{monotonicity}: if $p