These are my notes on the lecture Probability Theory,
taught by Prof.~\textsc{Chiranjib Mukherjee}
in the summer term 2023 at the University Münster.

\begin{warning}
    This is not an official script.
    The official lecture notes can be found on
    \href{https://sso.uni-muenster.de/LearnWeb/learnweb2/course/view.php?id=67595#coursecontentcollapse1}{Learnweb}.
\end{warning}

These notes contain errors almost surely.
If you find some of them or want to improve something,
please send me a message:\\
\texttt{notes\_probability\_theory@jrpie.de}.



\paragraph{Topics of this lecture}
\begin{enumerate}[(1)]
    \item Limit theorems: Laws of large numbers and the central limit theorem for i.i.d.~sequences,
    \item Conditional expectation and conditional probabilities,
    \item Martingales,
    \item Markov chains.
\end{enumerate}

This notes follow the way the material was presented in the lecture rather
closely. Additions (e.g.~from exercise sheets)
and slight modifications have been marked with $\dagger$.
