n. 1. a signed scalar associated with a vector and indicating both its magnitude and its sense but not its orientation. Two vectors AB and BA with resultant zero have measures of opposite polarity. See also norm. Compare length, metric. 2. a non-negative extended real-valued function defined on the subsets of a set that is additive, or more usually countably additive, for disjoint subsets and is zero for the empty set. The former is often called a finitely additive measure. If the function is permitted to take either sign, it is a signed measure. See also measure space, Lebesgue measure.