Regular measure information

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 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...

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

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

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} :...

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...

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...

{\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...

its radius and not on its centre. By convention, the measure is also required to be Borel regular, and to take positive and finite values on open balls...

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

that it be regular, that is: For almost all x, A ↦ κ Y ∣ X ( x , A ) {\displaystyle A\mapsto \kappa _{Y\mid X}(x,A)} is a probability measure For all A...

In measure theory, a branch of mathematics, a finite measure or totally finite measure is a special measure that always takes on finite values. Among finite...

In measure theory, a branch of mathematics, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a...

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...

\}.} regular if it is both inner regular and outer regular. a Borel regular measure if it is a Borel measure that is also regular. a Radon measure if it...

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

exist in every dimension: Regular simplex Measure polytope (Hypercube) Cross polytope (Orthoplex) Any other regular polytope is said to be exceptional. In...

condition to be a regular measure. μ is never a strictly positive measure, regardless of (X, Σ), since every measurable set has zero measure. Since μ(X) = 0...

doctrine" and "affirm the rule or measure of the Scripture." As compared to General Baptists or Free Baptists, Regular Baptists were strict in their beliefs...

Fijian poet is poetry with every verse ending with the same vowel of regular measure, which in practice is often achieved with poetic license through the...

definition of a pint differs by country, thus a pint glass will reflect the regular measure of beer in that country. In the UK, law stipulates that a serving of...