Title

Expectations for coherent probabilities

Date of Award

2002

Availability

Article

Degree Name

Doctor of Philosophy (Ph.D.)

Department

Mathematics

First Committee Member

Subramanian Ramakrishnan - Committee Chair

Abstract

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.

Keywords

Mathematics; Statistics

Link to Full Text

http://access.library.miami.edu/login?url=http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3056618

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