Harrington's game and measurability of regular tree languages

I will present some investigations on measure properties of regular tree languages. The motivation for this research comes from the dissertation of Matteo Mio. I plan to focus on two aims: the first aim is to show how to derive certain set theoretic properties from the assumption of determinacy of an appropriate game. The second aim is to present an intriguing interplay between measurability and basic concepts of mu-calculus.