PlanetMath: singular measure

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singular measure

(Definition)

Two measures $\mu$ and $\nu$ in a measurable space $(\Omega,\mathcal{A})$ are called singular if there exist two disjoint sets and in $\mathcal{A}$ such that $A\cup B =\Omega$ and $\mu(B)=\nu(A) = 0$ . This is denoted by $\mu\perp\nu$ .

"singular measure" is owned by Koro.

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Cross-references: disjoint, measurable space, measures
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This is version 4 of singular measure, born on 2003-02-09, modified 2003-02-10.
Object id is 4002, canonical name is SingularMeasures.
Accessed 4621 times total.

Classification:

AMS MSC:

28A12 (Measure and integration :: Classical measure theory :: Contents, measures, outer measures, capacities)

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