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