For an ergodic measure-preserving T with a finite generating partition P, the normalised information content −(1/n) log μ(P^(n)(x)) of the P-cylinder containing x up to time n converges μ-a.e. (and in L¹) to the Kolmogorov–Sinai entropy…
For an ergodic measure-preserving T with a finite generating partition P, the normalised information content −(1/n) log μ(P^(n)(x)) of the P-cylinder containing x up to time n converges μ-a.e. (and in L¹) to the Kolmogorov–Sinai entropy…