(mathematical analysis, measure theory) A measure-like function derived from some premeasure as follows: when it is applied to a set E, it yields the infimum of the premeasures of all possible premeasurable covers of E. More abstractly, a measure-like function whose domain is the power set of some underlying set, which has the properties of (1) yielding zero when applied to the empty set, (2) being monotonic (if A is subset of B then this function applied to A is less-than-or-equal to this function applied to B), (3) being subadditive (if A is a countable sum of Bⱼ's then this function applied to A is less-than-or-equal to the sum of the applications of this function to the Bⱼ's).

past participle of measure the drapes

Third-person singular simple present indicative form of measure the drapes

To an equal extent.

a kitchen utensil used primarily to measure small volumes of liquid or bulk solid cooking ingredients.

(statistics) A generalization of the canonical ensemble to infinite systems, giving the probability of a given system being in a given state (or, equivalently, of a given random variable having a given value).

plural of Gibbs measure

(statistics, probability) A measure of location for a batch, a sample, or a distribution characterizing a value around which are spread the members or the distribution.

plural of measure of central tendency

(mathematical analysis) A set, in a measurable space, that is expressible as a countable union of sets of finite measure.