BERNOULLI’S THEOREM AND KOLMOGOROV’S REQUEST FOR THE PROXIMITY OF PROBABILITY AND FREQUENCES
Vladimir Moiseevich Reznikov1,2
1Novosibirsk National Research State University, 2, Pirogov st., Novosibirsk, 630090, Russia
2Institute of Philosophy and Law, SB RAS, 8, Nikolaev st. Novosibirsk, 630090
Keywords: частотная интерпретация, субъективистская интерпретация, теорема Бернулли, близость вероятности и частот, устойчивость частот, принцип Курно, Колмогоров, Мизес, Борель, Фреше, Леви, frequency interpretation, subjectivist interpretation, Bernoulli theorem, proximity of probability and frequencies, stability of frequencies, Cournot principle, Kolmogorov, Mises, Borel, Frechet, Levy
Abstract
The famous mathematicians Borel, Levy and others criticized Kolmogorov’s request for the proximity of event probability and its frequency characteristics in the context of applying the probability theory. They believed this request to be redundant, since it is the conclusion of Bernoulli’s theorem. The article shows that within the frequency interpretation, Kolmogorov’s condition is not the conclusion of the theorem, but it is fulfilled as a consequence of frequency stability. In addition, we show that the deduction of Kolmogorov’s request made within the subjectivist interpretation is not justified within the frequency one.
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