ABSTRACT
The probability of an outcome was taken to be something closely related to the frequency with which that outcome could be expected to occur in a large number of identical repeated trials of some specified kind. A fundamental theorem of probability theory, Bayes' Theorem, relates the probability of a hypothesis on the basis of evidence to the conditional probability of the evidence, given the truth of the hypothesis and the initial probability that the hypothesis is true. "Nonpathological" means, essentially, that the initial probability distribution will give probability zero to any region of microconditions that have zero probability in the familiar, standard measure. Any non-pathological initial probability distribution for a mixing system will, as time goes into past infinity, also evolve into a probability distribution that is coarsely like the equilibrium distribution. The probability distribution is rationalized by showing that it is the uniquely stationary one that gives probability zero to regions given probability zero in that very natural measure.
