\documentclass{article}
\include{macros}
\begin{document}

% lecture number : lecture title : scribe
\lecture{0}{Notation}{Charless C. Fowlkes}{fowlkes@eecs.berkeley.edu}



% some symbols defined in stat205macros you will probably want to use

We will use the following notation

\[
\begin{array}{rl}
\Z & \mbox{the integers} \\
\Q & \mbox{the rational numbers} \\
\R & \mbox{the real numbers} \\
\Rn & \mbox{product of n copies of } \R \\
\P & \mbox{probability measure} \\
\E & \mbox{expectation} \\
\1_X & \mbox{indicator of } X \\
\var & \mbox{Variance} \\
\borel(\R) & \mbox{the borel sigma field} \\
\G,\F,\H & \mbox{some other sigma fields} \\
\L^2 & \mbox{the space of square integrable functions} \\
X_n \ascv X & \mbox{almost sure convergence} \\
X_n \pcv X & \mbox{convergence in probability} \\
X_n \ltcv X & \mbox{convergence in} \L^2 \\
X \ci_A Y & \mbox{conditional independence} \\
\end{array}
\]



% these gives definitions, theorems, etc. with numbering that
% correspond to the lecture number given above.

Definitions will look like

\begin{definition}
We define one to equal 1
\end{definition}

theorems like

\begin{theorem}
one and one is 1.
\end{theorem}

and proofs

\begin{proof} 
$\mbox{one and one} = 1 \wedge 1 = 1$
$\mbox{and one} = 1 \wedge 1 = 1$
$\mbox{and one} = 1 \wedge 1 = 1$
$\mbox{and one} = 1 \wedge 1 = 1$
$\mbox{and one} = 1 \wedge 1 = 1$
$\mbox{and one} = 1 \wedge 1 = 1$
\end{proof}

with the traditional \ \rule{2mm}{2mm} \  denoting the end of the proof.
\end{document}