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Convergence of Logarithmic Return Times 2408-2005

Foreword The last nine months of my study were dedicated to writing this master thesis. After having determined that I wanted it to be based on the course of Ergodic Theory, that I took in the first semester of the academic year 2003/2004, Karma Dajani suggested the subject of repetitions in number expansions. The subject interested me right from the start. Since in general writing my master thesis has been a nice experience, I would like to thank a few people who made this possible. First of all, I would like to thank my supervisor, Karma Dajani, for all the time and effort she put into discussing with me, advising me and correcting me. Without her help I'm sure writing my master thesis would have been much more stressful and difficult. I would also like to thank Byong Ki Seo for the time he took to explain to me parts of his doctoral thesis. Furthermore, I would like to thank all my friends for their support, especially in the last two months of the process and in particular I would like to thank Maarten van Pruijssen, who, besides moral support, also provided me with mathematical advise during our morning coffees and studying sessions. And finally I would like to thank my family and especially my parents for having an endless amount of faith in me.