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 f ...
of
probability theory
Probability theory 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 expressing it through a set o ...
that states that the
probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...
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
Unity may refer to:
Buildings
* Unity Building, Oregon, Illinois, US; a historic building
* Unity Building (Chicago), Illinois, US; a skyscraper
* Unity Buildings, Liverpool, UK; two buildings in England
* Unity Chapel, Wyoming, Wisconsin, US; a h ...
); 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.
References
{{DEFAULTSORT:Unit Measure
Probability theory