information:highlighting, structural:summarization, linguistic:paraphrasing
History

Before 1933, independence, in probability theory, was defined in a verbal manner. For example, de Moivre gave the following definition: “Two events are independent, when they have no connexion one with the other, and that the happening of one neither forwards nor obstructs the happening of the other”. If there are n independent events, the probability of the event, that all of them happen was computed as the product of the probabilities of these n events. Apparently, there was the conviction, that this formula was a consequence of the above definition. (Sometimes this was called the Multiplication Theorem.), Of course, a proof of his assertion cannot work without further more formal tacit assumptions.

The definition of independence, given in this article, became the standard definition (now used in all books) after it appeared in 1933 as part of Kolmogorov's axiomatization of probability. Kolmogorov credited it to S.N. Bernstein, and quoted a publication which had appeared in Russian in 1927.

Unfortunately, both Bernstein and Kolmogorov had not been aware of the work of the Georg Bohlmann. Bohlmann had given the same definition for two events in 1901 and for n events in 1908 In the latter paper, he studied his notion in detail. For example, he gave the first example showing that pairwise independence does not imply imply mutual independence.Even today, Bohlmann is rarely quoted. More about his work can be found in On the contributions of Georg Bohlmann to probability theory from de:Ulrich Krengel.