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In mathematics, a regular measure on a topological space is a measure for which every measurable set can be approximated from above by open measurable...

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...

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

In mathematics, an inner regular measure is one for which the measure of a set can be approximated from within by compact subsets. Let (X, T) be a Hausdorff...

Regular semigroup, related to the previous sense *-regular semigroup Borel regular measure Cauchy-regular function (or Cauchy-continuous function,) a continuous...

hypermeasure, large-scale or high-level measure, or measure-group is a metric unit in which, generally, each regular measure is one beat (actually hyperbeat)...

all compact K ⊆ G {\displaystyle K\subseteq G} . The measure μ {\displaystyle \mu } is outer regular on Borel sets S ⊆ G {\displaystyle S\subseteq G} :...

include: Borel measure, Jordan measure, ergodic measure, Gaussian measure, Baire measure, Radon measure, Young measure, and Loeb measure. In physics an...

Measure for Measure is the fourth studio album by the Australian rock/synth-pop band Icehouse, released in April 1986 in Australia by Regular Records...

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...

condition to be an inner regular measure, since singleton sets such as {x} are always compact. Hence, δx is also a Radon measure. Assuming that the topology...

regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons...

{\displaystyle C} . If a Borel measure μ {\displaystyle \mu } is both inner regular and outer regular, it is called a regular Borel measure. If μ {\displaystyle...

The Canons Regular of St. Augustine are priests who live in community under a rule (Latin: regula and κανών, kanon, in Greek) and are generally organised...

{\displaystyle \mu } may either be said to be a tight measure or to be an inner regular measure. If Y {\displaystyle Y} is an X {\displaystyle X} -valued random variable...

Lebesgue–Stieltjes measure, which may be associated to any function of bounded variation on the real line. The Lebesgue–Stieltjes measure is a regular Borel measure, and...

specifically, in geometric measure theory — spherical measure σn is the "natural" Borel measure on the n-sphere Sn. Spherical measure is often normalized so...

their 3-dimensional analogues, the convex regular 4-polytopes can be naturally ordered by size as a measure of 4-dimensional content (hypervolume) for...

mathematics, a locally finite measure is a measure for which every point of the measure space has a neighbourhood of finite measure. Let ( X , T ) {\displaystyle...

Lebesgue measure Lebesgue integration Lebesgue's density theorem Counting measure Complete measure Haar measure Outer measure Borel regular measure Radon...