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Dynamical systems on measure spaces, invariant measures, ergodic averages, mixing properties.
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Density-$c_0$ in $\ell^\infty$
Let $A \subseteq \mathbb{N}$, define the upper density of $A$ as,
$$
\overline{\delta}(A) := \limsup_{N\to\infty}\frac{|A\cap\{1,2,3,\cdots,N\}|}{N}.
$$
This naturally leads to a weaker form of conve …