One-sided generator
= One-sided generator
A one-sided generator is a <measurable partition> $\xi$ with $\sigma(\bigvee_{j\ge0}T^{-j}\xi)=\mathcal B$ modulo null sets. Equivalently, every measurable set can be approximated in measure by unions of atoms of finite forward-name blocks. A one-sided coordinate partition generates a one-sided <Bernoulli shift>; for a nontrivial base distribution, it does not generate the two-sided version, whose negative coordinates are independent of the nonnegative ones.