 Generating measurable partition

For an invertible measure-preserving system, a generating measurable partition $\xi$ has $\sigma ({\bigvee }_{j\in \mathbb{Z}}{T}^{-j}\xi )=\mathcal{B}$ modulo null sets. Thus knowing the entire two-sided itinerary determines all measurable observations. A finite or countable finite-entropy generating partition computes the system entropy through the Kolmogorov-Sinai generator theorem.