Güleken, Ayşe Işıl2022-08-222022-08-222022-072022-072022-08-19http://hdl.handle.net/11693/110462Cataloged from PDF version of article.Thesis (Master's): Bilkent University, Department of Mathematics, İhsan Doğramacı Bilkent University, 2022.Includes bibliographical references (leave 44-45).Haar systems are generalizations of Haar measures on groups to groupoids. Naturally, important research directions in the field try to generalize the well known existence of a Haar measure on a locally compact group to the existence of Haar systems in different groupoid settings. The groupoid case differs significantly from the group case, evidenced by a result of Deitmar, showing that non-existence is possible even for compact groupoids. We first present the classical theory of locally compact groups and Haar Measures on them. We motivate our investigation by constructing full C∗-algebras on locally compact groups, which uses the existence of Haar measures. Then, we cover the theory of locally compact groupoids and present Renault's result that provides a complete characterization of the existence of Haar systems for the r-discrete locally compact groupoid setting, which are precisely the ones where the range map is a local homeomorphism. We present a question from Williams that investigates if the open range map assumption is redundant for second countable, locally compact and transitive groupoids. Finally, we present Buneci's counter-example that answers this question in the negative.vi, 45 leaves ; 30 cm.Englishinfo:eu-repo/semantics/openAccessHaar systemsLocally compact groupoidsr-discrete groupoidsThesisB161180