outer measure
（ plural ）
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(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).
outer measure
The outer measure assigns to each subset the infimum of the premeasures of all countable covers by premeasurable sets, ensuring monotonicity, subadditivity, and that the empty set has measure zero.
The outer measure assigns to each subset the infimum of the premeasures of all countable covers by premeasurable sets, ensuring monotonicity, subadditivity, and that the empty set has measure zero.
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