ABSTRACT
Historically, probability theory seems to have begun with investigations into “games of chance,” the traditional framework for many models and applications in what is now called “discrete” probability theory. The probability of an outcome with a given property, or “event,” is defined as the ratio of the number of possible outcomes which possess the given property, to the total number of all outcomes possible. The convergence of probability theory and measure theory occurred first in the work of Andrey Kolmogorov in his Foundations of the Theory of Probability in 1933. Probability measures on ℝ are commonly induced by more general probability spaces. But such measures can also arise in a specific application for which ℝ is the appropriate sample space. As for discrete probability theory, there are also infinitely many probability measures on ℝ under the continuous theory, all of which are then Borel measures.
