2017
Том 69
№ 9

All Issues

Descriptive Estimates for a Set of Points That Approximate an Ergodic Measure

Sivak A. G.


Abstract

We obtain descriptive estimates for a set of points that approximate an ergodic invariant measure of a continuous mapping on a compact set. For example, in the case of a metrically transitive mapping with an invariant measure equivalent to the Lebesgue measure, we prove that a set of points generating invariant measures with maximum support contains a dense G δ-set, whereas, in the general case, one has a much worse estimate G δσδ.

English version (Springer): Ukrainian Mathematical Journal 55 (2003), no. 6, pp 987-992.

Citation Example: Sivak A. G. Descriptive Estimates for a Set of Points That Approximate an Ergodic Measure // Ukr. Mat. Zh. - 2003. - 55, № 6. - pp. 817-823.