Ensemble, mesure et probabilité selon Emile Borel. (Set, measure and probability according to Emile Borel). (French) Zbl 0714.01016

Callens, Stéphane

Math. Inf. Sci. Hum. 110, 27-45 (1990).

The aim of this paper is to try to answer the following question: why Emile Borel dedicated himself to the theory of probability suddenly about 1905? After analyzing three possible replies, in the form of three imagined biographies, the first one written by an analyst, the second one by a political historian and the third one by a scientific philosopher, the author proposes as a clue the use of the continued fractions in Borel writings. He also considers the influence of Cantor’s theory of sets and then describes Borel’s contributions to the concepts of rarefaction. The paper contains large excerpts from Borel papers or books on probability.

Reviewer: J.Mawhin

MSC:

01A60

History of mathematics in the 20th century

Keywords:

probability; measure. continued fractions; theory of sets