Abstract:We study the descriptive complexity of sets of points defined by placing restrictions on statistical behaviour of their orbits in dynamical systems on Polish spaces. A particular examples of such sets are the set of generic points of a T -invariant Borel probability measure, but we also consider much more general sets (for example, α-Birkhoff regular sets and the irregular set appearing in multifractal analysis of ergodic averages of a continuous realvalued function). We show that many of these sets are Borel.… Show more
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