In mathematics, a nonmeasurable set is one for which the \"volume\" cannot be assigned. This \"volume\" can be understood differently depending on the structure in which we search sucha a set. In fact, from the very beginning, the notation of nonmeasurable set was a source of considerable controversy.

CONTENTS

Introduction\nI\n1. Preliminaries\n2. nonmeasurable sets\nII\n3. Kuratowski partitions\n4. On Kuratowski partitions in tree structures\n5. On Kuratowski partitions in Ellentuck topology\n6. Ideals associated with Kuratowski partitions\n7. Kuratowski partitions in Baire spaces\n8. Kuratowski partitions and game theory\n9. Kuratowski partitions in complete metric spaces\n10. An example of a metric space without Kuratowski partitions\nIII\n11. The generalization of Louveau-Simpson Theorem\n12. On the equivalences of Gitik-Shelak Theorem\n13. The generalization of Halpern-Lauchli Theorem\nIV\n14. {Partitions and point-finite covers in Baire spaces\n15. Nonmeasurable unions for point-finite families\n16. On the existence of measurable selectors\nBibliography\nIndex