@article{GOGACZ2017108,
    Abstract = {We investigate measure theoretic properties of regular sets of infinite trees. As a first result, we prove that every regular set is universally measurable and that every Borel measure on the Polish space of trees is continuous with respect to a natural transfinite stratification of regular sets into {$\omega$}1 ranks. We also expose a connection between regular sets and the σ-algebra of R-sets, introduced by A. Kolmogorov in 1928 as a foundation for measure theory. We show that the game tree languagesWi,k are Wadge-complete for the finite levels of the hierarchy of R-sets. We apply these results to answer positively an open problem regarding the game interpretation of the probabilistic {$\mu$}-calculus.},
    Author = {Gogacz, Tomasz and Michalewski, Henryk and Mio, Matteo and Skrzypczak, Micha{\l}},
    File = {sk17\_measure\_trees (0) (0) - a - a - r.pdf},
    ISSN = {0890-5401},
    Journal = {Information and Computation},
    Keywords = {Regular tree languages, Measure theory, Topological complexity},
    Pages = {108 - 130},
    Title = {Measure properties of regular sets of trees},
    URL = {http://www.sciencedirect.com/science/article/pii/S0890540117300627},
    Volume = {256},
    Year = {2017},
    bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0890540117300627},
    bdsk-url-2 = {https://doi.org/10.1016/j.ic.2017.04.012},
    date-added = {2019-03-14 18:55:13 +0100},
    date-modified = {2019-03-14 18:55:13 +0100},
    doi = {10.1016/j.ic.2017.04.012}
}

@article{GOGACZ2017108, Abstract = {We investigate measure theoretic properties of regular sets of infinite trees. As a first result, we prove that every regular set is universally measurable and that every Borel measure on the Polish space of trees is continuous with respect to a natural transfinite stratification of regular sets into {$\omega$}1 ranks. We also expose a connection between regular sets and the σ-algebra of R-sets, introduced by A. Kolmogorov in 1928 as a foundation for measure theory. We show that the game tree languagesWi,k are Wadge-complete for the finite levels of the hierarchy of R-sets. We apply these results to answer positively an open problem regarding the game interpretation of the probabilistic {$\mu$}-calculus.}, Author = {Gogacz, Tomasz and Michalewski, Henryk and Mio, Matteo and Skrzypczak, Micha{\l}}, File = {sk17_measure_trees (0) (0) - a - a - r.pdf}, ISSN = {0890-5401}, Journal = {Information and Computation}, Keywords = {Regular tree languages, Measure theory, Topological complexity}, Pages = {108 - 130}, Title = {Measure properties of regular sets of trees}, URL = {http://www.sciencedirect.com/science/article/pii/S0890540117300627}, Volume = {256}, Year = {2017}, bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0890540117300627}, bdsk-url-2 = {https://doi.org/10.1016/j.ic.2017.04.012}, date-added = {2019-03-14 18:55:13 +0100}, date-modified = {2019-03-14 18:55:13 +0100}, doi = {10.1016/j.ic.2017.04.012} }