Cantor Bernoulli measure
= Cantor Bernoulli measure
{c}
{title2=$\nu$}
The law of $\sum_{j\geq1}2\omega_j3^{-j}$, for independent fair binary digits $\omega_j$, is supported on the <Cantor set>. It is invariant and ergodic under $T_3$, as the image of a <Bernoulli shift>. Each permitted ternary cylinder of length $n$ has measure $2^{-n}$, giving entropy rate $\log2$. The <Host equidistribution theorem> makes almost every point a <normal number> in base $2$, while its ternary digits omit $1$.