论文标题
Banach-Tarski悖论
The Banach-Tarski Paradox
论文作者
论文摘要
本文提出了基于豪斯多夫悖论的Banach-Tarski悖论的强烈和弱形式。它提供了现代化的悖论和矛盾和悖论集的悖论和必要特性。悖论的量度理论的历史意义及其对Banach和Tarski的不正确归属。最后，讨论了选择的公理的必要性，并与其他能够悖论的公理和拓扑假设进行了对比。
This thesis presents the strong and weak forms of the Banach-Tarski paradox based on the Hausdorff paradox. It provides modernized proofs of the paradoxes and necessary properties of equidecomposable and paradoxical sets. The historical significance of the paradox for measure theory is covered, along with its incorrect attribution to Banach and Tarski. Finally, the necessity of the axiom of choice is discussed and contrasted with other axiomatic and topological assumptions that enable the paradoxes.
