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regular measure
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(Definition)
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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 $A' \in \mathcal{B}(X)$ with $A' \subset G - K$ , one has $\mu_R(A') <\varepsilon$ .
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"regular measure" is owned by bci1.
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Cross-references: open subset, compact subset, measure, topological space
This is version 2 of regular measure, born on 2008-09-15, modified 2008-09-15.
Object id is 11029, canonical name is RegularMeasure.
Accessed 760 times total.
Classification:
| AMS MSC: | 28A10 (Measure and integration :: Classical measure theory :: Real- or complex-valued set functions) | | | 28A12 (Measure and integration :: Classical measure theory :: Contents, measures, outer measures, capacities) | | | 28C15 (Measure and integration :: Set functions and measures on spaces with additional structure :: Set functions and measures on topological spaces ) |
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Pending Errata and Addenda
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