Basics of measure and probability theory

Abstract

The first use of mathematics to solve probability problems goes back to 1654 with the works of Fermat and Pascal. Their joint effort was motivated by questions raised by Antoine Gombaud, Chevalier de Méré, who was interested in betting strategies in the context of dice games. One of his main questions was: Is the probability of getting at least one double six when rolling two fair dice 24 times larger or smaller than one-half? A few years later, Huygens wrote the first book in probability theory [46] while, since the beginning of the 18th century, a number of mathematicians, including Bernoulli, de Moivre, Laplace, Poisson and Chebyshev, have made major discoveries in this field. But the most important turn in the history of probability since Fermat and Pascal is certainly the publication of Kolmogorov’s monograph [56] in 1933 which defines the axiomatic foundations of probability theory and marks the beginning of modern probability. For an English translation, see [58]. Though this point of view might be simplistic, the main idea of his work was to redefine probability concepts from their analog in measure theory.