6. Furstenberg's Theorem
We begin by proving Furstenberg's Theorem, which tells us that if $f \colon X \to X$ is a weakly mixing system then any $n$-fold product
$$ f \times \cdots \times f \colon X \times \cdots \times X \to X \times \cdots \times X $$
is automatically transitive.
Afterwards we introduce linear dynamical systems on Banach spaces, and construct an example of a linear dynamical system that is weakly mixing but not mixing.
Here are today's notes:
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