Unit measure is an
axiom
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or ...
of
probability theory
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...
that states that the
probability
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...
of the entire
sample space
In probability theory, the sample space (also called sample description space, possibility space, or outcome space) of an experiment or random trial is the set of all possible outcomes or results of that experiment. A sample space is usually den ...
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
[T. Oldberg and R. Christensen "Erratic measure" NDE for the Energy Industry 1995, American Society of Mechanical Engineers, New York, NY.] 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
{{DEFAULTSORT:Unit Measure
Probability theory