In the mathematical field of measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the...

subset E ⊆ R {\displaystyle E\subseteq \mathbb {R} } , the Lebesgue outer measure λ ∗ ( E ) {\displaystyle \lambda ^{\!*\!}(E)} is defined as an infimum...

In mathematics, a metric outer measure is an outer measure μ defined on the subsets of a given metric space (X, d) such that μ ( A ∪ B ) = μ ( A ) + μ...

In mathematics, an outer measure μ on n-dimensional Euclidean space Rn is called a Borel regular measure if the following two conditions hold: Every Borel...

on all compact sets, outer regular on all Borel sets, and inner regular on open sets. These conditions guarantee that the measure is "compatible" with...

specifically fractals and their Hausdorff dimensions. It is a type of outer measure, named for Felix Hausdorff, that assigns a number in [0,∞] to each set...

via the Lebesgue measure. In the one-dimensional case, the Lebesgue outer measure of a set is defined in terms of the lengths of open intervals. Concretely...

Lebesgue measure Lorentz space Lifting theory Measurable cardinal Measurable function Minkowski content Outer measure Product measure Pushforward measure Regular...

Borel measure μg on [a, b] which agrees with w on every interval I. The measure μg arises from an outer measure (in fact, a metric outer measure) given...

points have measure 0 {\displaystyle 0} , so the measure of any compact subset of this vertical segment is 0 {\displaystyle 0} . But, using outer regularity...