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СпутникиРНSpaceXРоскосмосNASAThe 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.
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.
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U.Strathclyde, Glasgow, Scotland, G40GE, UK
A. Deshpande
A.D. is sole author
Corresponding authorCorrespondence to A. Deshpande.
The authors declare no competing interests.
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Deshpande, A. A Simple Proof of Kolmogorov’s 0-1 Law. Sankhya A (2026). https://doi.org/10.1007/s13171-026-00445-w
Received: 02 July 2026
Accepted: 06 July 2026
Published: 22 July 2026
Version of record: 22 July 2026
DOI: https://doi.org/10.1007/s13171-026-00445-w