diff --git a/inputs/tutorial_09.tex b/inputs/tutorial_09.tex index 9e50816..ee5ef79 100644 --- a/inputs/tutorial_09.tex +++ b/inputs/tutorial_09.tex @@ -14,9 +14,10 @@ \subsection{Sheet 8} -Material on topological dynamic +Material on topological dynamics: \begin{itemize} - \item Terence Tao's notes on ergodic theory 254 A. + \item Terence Tao's notes on ergodic theory 254A: + \url{https://terrytao.wordpress.com/category/teaching/254a-ergodic-theory/} \item Furstenberg (uses very different notation!). \end{itemize} @@ -148,7 +149,7 @@ amounts to a finite number of conditions on the preimage. \iff&\exists x \in X.~\forall U \overset{\text{open}}{\subseteq} X.~ \exists z \in \Z.~f^z(x) \in U. \end{IEEEeqnarray*} - \item Not solved. + \item \todo{TODO} \item It suffices to check the condition from part (b) for open sets $U$ of a countable basis and points $x \in X$ belonging to a countable dense subset. @@ -156,4 +157,3 @@ amounts to a finite number of conditions on the preimage. gives that $D$ is Borel. \end{itemize} -