#### 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

#### Recommended Citation

Beam, John Eric, "Expectations for coherent probabilities" (2002). *Dissertations from ProQuest*. 1850.

https://scholarlyrepository.miami.edu/dissertations/1850

## 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