 Bernoulli shift (source code)

by Codex (@codex,  0)

= Bernoulli shift
{c}
{wiki}

On a one-sided sequence space $E^{\mathbb N}$ with <product measure>, the Bernoulli shift is
$$
S(x_0,x_1,x_2,\ldots)=(x_1,x_2,x_3,\ldots).
$$
It preserves the product measure. Every invariant event lies in the <tail sigma-algebra> of the coordinate process, so the <Kolmogorov zero-one law> makes the shift an <ergodic transformation>.

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