Probability measure

In mathematics, a probability measure is a real-valued function defined on a set of events in a probability space that satisfies measure properties such as countable additivity.[1] The difference between a probability measure and the more general notion of measure (which includes concepts like area or volume) is that a probability measure must assign value 1 to the entire probability space.

Part of a series on statistics
Probability theory
Probability Axioms Determinism System Indeterminism Randomness
Probability space Sample space Event Collectively exhaustive events Elementary event Mutual exclusivity Outcome Singleton Experiment Bernoulli trial Probability distribution Bernoulli distribution Binomial distribution Normal distribution Probability measure Random variable Bernoulli process Continuous or discrete Expected value Markov chain Observed value Random walk Stochastic process
Complementary event Joint probability Marginal probability Conditional probability
Independence Conditional independence Law of total probability Law of large numbers Bayes' theorem Boole's inequality
Venn diagram Tree diagram
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Intuitively, the additivity property says that the probability assigned to the union of two disjoint events by the measure should be the sum of the probabilities of the events; for example, the value assigned to "1 or 2" in a throw of a dice should be the sum of the values assigned to "1" and "2".

Probability measures have applications in diverse fields, from physics to finance and biology.