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.

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[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.