Unit measure

Unit measure is an axiom of probability theory^[1] that states that the probability of the entire sample space is equal to one (unity); that is, P(S)=1 where S is the sample space. Loosely speaking, it means that S must be chosen so that when the experiment is performed, something happens. The term measure here refers to the measure-theoretic approach to probability.

Violations of unit measure have been reported in arguments about the outcomes of events^[2]^[3] under which events acquire "probabilities" that are not the probabilities of probability theory. In situations such as these the term "probability" serves as a false premise to the associated argument.

References

^ A. Kolmogorov, "Foundations of the theory of probability" 1933. English translation by Nathan Morrison 1956 copyright Chelsea Publishing Company.
^ R. Christensen and T. Reichert: "Unit measure violations in pattern recognition: ambiguity and irrelevancy" Pattern Recognition, 8, No. 4 1976.
^ T. Oldberg and R. Christensen "Erratic measure" NDE for the Energy Industry 1995, American Society of Mechanical Engineers, New York, NY.

[1] A. Kolmogorov, "Foundations of the theory of probability" 1933. English translation by Nathan Morrison 1956 copyright Chelsea Publishing Company.

[2] R. Christensen and T. Reichert: "Unit measure violations in pattern recognition: ambiguity and irrelevancy" Pattern Recognition, 8, No. 4 1976.

[3] T. Oldberg and R. Christensen "Erratic measure" NDE for the Energy Industry 1995, American Society of Mechanical Engineers, New York, NY.

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