= Bernoulli coordinate observable is not almost periodic
{c}
{title2=$\|U^nf-U^mf\|_2^2=2\quad(n\ne m)$}
For independent fair signs on a two-sided <Bernoulli shift>, the coordinate observable $f(y)=y_0$ has unit norm and pairwise orthogonal orbit values. Their pairwise squared distance is two, excluding a finite small net in global $L^2$. Its pullback along a <factor map> can nevertheless be a <relatively almost periodic observable>, since it is fiber-constant and takes only two values.
Back to article page
