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. 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 1 to the entire probability space.
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, e.g. the value assigned to "1 or 2" in a throw of a die 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.
Read more about Probability Measure: Definition, Example Applications
Famous quotes containing the words probability and/or measure:
“The source of Pyrrhonism comes from failing to distinguish between a demonstration, a proof and a probability. A demonstration supposes that the contradictory idea is impossible; a proof of fact is where all the reasons lead to belief, without there being any pretext for doubt; a probability is where the reasons for belief are stronger than those for doubting.”
—Andrew Michael Ramsay (1686–1743)
“Trying to love your children equally is a losing battle. Your children’s scorecards will never match your own. No matter how meticulously you measure and mete out your love and attention, and material gifts, it will never feel truly equal to your children. . . . Your children will need different things at different times, and true equality won’t really serve their different needs very well, anyway.”
—Marianne E. Neifert (20th century)