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- W99381712 abstract "This chapter focuses on the concepts of events, probability, independence, and conditional probability. The Kolmogorov setup for probability consists of a probability space (Ω, F, P) having as components a sample space, Ω; a σ-field F of selected subsets of Ω; and a probability measure or assignment, P. The sample space Ω has elements ω called the elementary events. The probability measure P is a set function from F to the interval, and it satisfies the following four axioms: (1) unit normalization, (2) non-negativity, (3) finite additivity, and (4) continuity. Kolmogorov proposed a definition of stochastic independence, relating the notion of axiomatic probability to informal or intuitive ideas of unrelated, unlinked, or independent events or experiments. He also proposed a definition of conditional probability, relating axiomatic probability to an informal idea of the effect of the knowledge of the outcome of an event on the uncertainties, or chances, of the outcomes of other events. The (Ω, F, P) model and associated definitions are deemed by many to be virtually universally applicable in those situations where one has to deal with chance or uncertainty. The empirical meaningfulness of the probability scale is explicated through measurement theory." @default.
- W99381712 created "2016-06-24" @default.
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- W99381712 date "1973-01-01" @default.
- W99381712 modified "2023-10-16" @default.
- W99381712 title "Axiomatic Quantitative Probability" @default.
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- W99381712 doi "https://doi.org/10.1016/b978-0-12-256450-5.50006-6" @default.
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