Definition 40.1.17 (Bernoulli Shift).label Let $G$ be a group, $X = 2^{G}$ equipped with the product topology, and
\[\alpha: X \to X \quad \alpha_{g}(x)(h) = x(g^{-1}h)\]
Viewing $2^{G}$ as the power set of $G$, $\alpha_{g}(A) = gA$ for any $A \subset G$. The $G$-flow $G \curvearrowright X$ is the Bernoulli shift of $G$, and $G$-subflows of $X$ are subshifts of $G$.
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