Collapse Volume VIII, 959–1000

Chapter

A Formal Deduction of the Market

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EXCERPT

Kolmogorov’s probability formalism is pure mathematics and knows nothing of experiment, trial, event, or realization. It is an abstract measure theory in which a function, called measure or probability, maps a field of sets into the set of positive numbers and verifies certain axioms of additivity. The passage to the limit in countable sums of measurable sets and the notion of sets of measure zero are its main characteristics. Random variables are mappings between the sample space (the set of elementary events) and the real set, and are said to be measurable as soon as the pre-images of the mapping are measurable…