AI 中文总结
本文将柯尔莫哥洛夫0-1律视作逻辑中的假真律，简化了其证明，且在概率论基础结果的证明中引入了逻辑的应用。
AI 中文摘要
柯尔莫哥洛夫0-1律是概率论中极为强大且基础的定律，大数定律的结果是其推论，而大数定律是现代统计机器学习的理论基石。人们对该定律证明的兴趣预期复苏，却因它的测度论属性而受阻。通过将0-1律视为类似逻辑中的假真律，本文证明该定律的证明可被简化，这种简化源于我们的方法几乎无需超出定义明显概率空间所需的测度论知识。本文的一项新贡献是在概率论基础结果的证明中运用了逻辑。
英文摘要
The Kolmogorov's 0-1 law is so powerful and fundamental in Probability theory that the result of the law of large numbers is its corollary. The latter is the theoretical bedrock of modern day statistical machine learning. Expected resurgence in the interest of the law's proof is challenged by its measure theoretic nature. By observing 0-1 law as False-Truth law like in logic, we show here that the proof of the law is simplified. This simplicity comes from the fact that our approach hardly needs any measure theory beyond defining an obvious probability space. A novel contribution via this article is the use of logic within the proof of a fundamental result in the theory of probability.
DOI：10.1007/s13171-026-00445-w
