Expectations for coherent probabilities
Date of Award
Doctor of Philosophy (Ph.D.)
First Committee Member
Subramanian Ramakrishnan, Committee Chair
In the 1930's, Kolmogorov borrowed the axiomatic system of the Lebesgue measure as a foundation for what is now the standard theory of probability. The domain of the probability measure is assumed to possess the structure of a Boolean sigma-algebra, and the measure is assumed to be countably additive. The "expectation of a random variable" is developed as the integral of a measurable function. Around the same time as Kolmogorov's development, de Finetti introduced the notion of a "coherent" probability, consistent with the Lebesgue theory, but requiring neither countable additivity of the measure nor any sort of structure on its domain. In this thesis I present a theory of the integral, or expectation, with respect to this broader notion of a probability.
Beam, John Eric, "Expectations for coherent probabilities" (2002). Dissertations from ProQuest. 1850.