Unit measure

Short description: Axiom of probability theory

Not to be confused with Unit of measurement.

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.

## See also

* Overround, the amount by which the sum of the implied probabilities of a book exceeds 100%

## References

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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