General affine invariances related to Mahler volume are introduced. We establish their affine isoperimetric inequalities by using a symmetrization scheme that involves a total of $2n$ elaborately chosen Steiner symmetrizations at a time. The necessity of this scheme, as opposed to the usual Steiner symmetrization, is demonstrated with an example (see the Appendix).

中文翻译：

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与马勒体积相关的一般仿射不变性

介绍了与马勒体积有关的一般仿射不变性。我们通过使用一个对称化方案来建立它们的仿射等周不等式，该方案一次涉及总共 $2n$ 精心选择的 Steiner 对称化。与通常的 Steiner 对称化相反，该方案的必要性通过一个示例进行了说明（参见附录）。