Paradoxical Decompositions, or the Nonexistence of Finitely Additive Measures / Part I: |
Introduction / 1: |
The Hausdorff Paradox / 2: |
The Banach-Tarski Paradox: duplication spheres and balls / 3: |
Locally commutative actions: minimizing the number of pieces in a paradoxical decomposition / 4: |
Higher dimensions and non-Euclidean spaces / 5: |
Free groups of large rank: getting a continuum of spheres from one / 6: |
Paradoxes in low dimensions / 7: |
The semi-group of equideomposability types / 8: |
Finitely Additive Measures, or the Nonexistence of Paradoxical Decompositions / Part II: |
Transition / 9: |
Measures in groups / 10: |
Applications of amenability: Marczewski measures and exotic measures / 11: |
Growth conditions in groups and supramenability / 12: |
The role of the axiom of choice / 13: |
Paradoxical Decompositions, or the Nonexistence of Finitely Additive Measures / Part I: |
Introduction / 1: |
The Hausdorff Paradox / 2: |