Ouroboros Spaces: An Intuitive Approach to Self-Referential Functional Analysis with Applications to Probability Theory

Abstract

In this paper, we aim to introduce the concept of the Ouroboros space and the complimentary concept of the Ouroboros function by using the Ouroboros equation [1] as our starting point. We start with a few univariate definitions, and then move on to multivariate definitions. We contextualize and motivate these concepts with a few examples. Then, we discuss a few aspects from probability theory that are relevant to the idea of an Ouroboros space, eventually proving two critical theorems. We briefly introduce the case of mixed domains, and summarize our findings, while emphasizing the importance of self-referential functions.

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