Generating measurable partition
= 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>.