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# regular measure

###### Definition 0.1.

A regular measure $\mu_{R}$ on a topological space $X$ is a measure on $X$ such that for each $A\in\mathcal{B}(X)$ , with $\mu_{R}(A)<\infty$), and each $\varepsilon>0$ there exist a compact subset $K$ of $X$ and an open subset $G$ of $X$ with $K\subset A\subset G$, such that for all sets $A^{{\prime}}\in\mathcal{B}(X)$ with $A^{{\prime}}\subset G-K$, one has $\mu_{R}(A^{{\prime}})<\varepsilon$.

Keywords:

regular measure, Borel spaces

Related:

OuterMeasure

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

28C15*no label found*28A12

*no label found*28A10

*no label found*

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