独立随机变量的元非传递系统与分形
Meta-intransitive Systems of Independent Random Variables and Fractals
AI总结：
本文从推广非传递骰子的基本随机变量元组构造任意有限阶及无穷阶的元非传递系统，证明无穷阶系统为分形并可计算相似维数，同时提出维数上界问题。
摘要：
我们从推广非传递骰子的基本随机变量元组出发，构造任意有限阶的独立随机变量元非传递系统。在该构造下，只要某个线性泛函的等式对基本变量成立，该等式就被保持。这一方案还被推广到无穷阶系统，这些系统被证明是分形，并且可以计算其相似维数。文中提出了该维数上界的问题。
英文摘要：
We construct meta-intransitive systems of independent random variables of any finite order from basic tuple of random variables which generalize intransitive dice. Under this construction, the equality of some linear functional is preserved, provided this equality hold for the basic variables. This scheme is also extended to infinite-order systems, which are shown to be fractals, and for which the similarity dimension can be evaluated. The problem of the upper bound for this dimension is posed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
