Overview

Probability theory developed into a branch of abstract mathematics during the first 30 years of the twentieth century. Until the late nineteenth century probabilities were treated mostly in context, be it as the probability of testimony or arguments, of survival or death, of making errors in measurement, or in statistical mechanics. This is the era of classical probability. It was rife with paradoxes and had a low mathematical status. In the early twentieth century various efforts were made to develop a probability theory that was independent of applications and possessed a provably consistent structure. The theory that found near universal acceptance tied probability theory to measure theory. The Russian mathematician Andrei Kolmogorov (1903-1987) gave in 1933 a definitive axiomatic formulation of measure theoretic probability. Probability is now defined as a measure over an algebra of subsets of an abstract...