A Consistent Estimator of the Entropy of Measures and Dynamical Systems

In the paper, a new invariant of measures and dynamical systems, called statentropy, is described. A statistical estimator for statentropy, computed without using auxiliary estimates of measures, is constructed. It is proved that the proposed statistical estimator is consistent under fairly general restrictions. We show that for exact dimensional measures, statentropy coincides with the Hausdorff dimension of the measure, and for ergodic dynamical systems, it coincides with the metric entropy of the map.