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 set ...

Any Borel probability measure on a locally compact Hausdorff space with a countable base for its topology, or compact metric space, or Radon space, is regular. Definition · Examples · Inner regular measures that...

22 окт. 2017 г. · Measures only satisfy condition (1) are called Borel measures, and if (2) is satisfied as well are called Borel regular measures . A question about regularity of Borel measures Understanding regular Borel measures - Math Stack Exchange Why is Hausdorff measure Borel regular? - Math Stack Exchange Другие результаты с сайта math.stackexchange.com

Let be a Borel regular outer measure on a topological space X having the property that every closed set can be expressed as the countable intersection of open ...

22 апр. 2010 г. · Let X be a metric space. Then every Borel measure μ on X is regular (i.e. for every Borel set B and every ε > 0, there exists a closed set Fε ... About the definition of Borel and Radon measures - MathOverflow Is every finite Borel measure on a locally compact Hausdorff, σ ... Atoms of regular Borel measure - MathOverflow Regular Borel Measures equivalent definition - MathOverflow Другие результаты с сайта mathoverflow.net

16 авг. 2013 г. · In these three different contexts Borel regular measures are then defined as follows: (A) Borel measures μ for which sup{μ(C):C⊂E is closed}=μ(E) ...

11 окт. 2019 г. · Regular tight Borel measures are automatically Radon. A regular Borel measure need not be tight. A Borel measure μ \mu on a topological ...

An outer measure mu on R^n is Borel regular if, for each set X subset R^n, there exists a Borel set B superset X such that mu(B)=mu(X).

The existence of a regular Borel measure whose support is a given compact Hausdorff space X imposes definite struc- tures on X, C(X), and C(X)*.

We say that a Borel measure space (X, μ) is regular when (as agreed in Remark 1.7.6) μ(C) < ∞ for each compact set C and each measurable subset X0 differs from ...