Ouroboros 空间：一种用于自指泛函分析及其在概率论中应用的直观方法
泛函分析
2021-05-13 v3 概率论
摘要
在本文中，我们旨在以 Ouroboros 方程 [1] 为出发点，引入 Ouroboros 空间的概念以及补充性的 Ouroboros 函数概念。我们从一些单变量定义开始，然后转向多变量定义。我们通过若干例子对这些概念进行语境化并给出动机。接着，我们讨论概率论中与 Ouroboros 空间思想相关的若干方面，最终证明两个关键定理。我们简要介绍混合域的情形，并总结我们的发现，同时强调自指函数的重要性。
引用
@article{arxiv.2102.07854,
title = {Ouroboros Spaces: An Intuitive Approach to Self-Referential Functional Analysis with Applications to Probability Theory},
author = {Nathan Thomas Provost},
journal= {arXiv preprint arXiv:2102.07854},
year = {2021}
}
备注
In the first update, the citations were corrected. One of the authors' names in the first citation was incorrect, and has been corrected in this update. In the second update, Theorem 2 was revised and corrected. Initially, its statement contained an erroneous overgeneralization, which has now been corrected