PreprintCC BY 4.0arXiv
Kolmogorov's 0-1 law as false-truth law
Abstract
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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BibTeX
@misc{deshpande2026kolmogorovs,
title = {{Kolmogorov's 0-1 law as false-truth law}},
author = {A. Deshpande},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05048},
eprint = {2609.05048},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05048},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Kolmogorov's 0-1 law as false-truth law
AU - A. Deshpande
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.05048
UR - https://arxiv.org/abs/2609.05048
AB - 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.
ER -