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'Borel measure'
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| Title of object: |
Borel measure |
| Canonical Name: |
BorelMeasure |
| Type: |
Definition |
| Created on: |
2007-10-01 17:33:33 |
| Modified on: |
2008-04-12 13:57:50 |
| Classification: |
msc:28A10, msc:28A12, msc:28C15, msc:60A10 |
Revision comment (for changes between this and next version):
\bibitem{MRB2k6}
M.R. Buneci. 2006.,
\PMlinkexternal{Groupoid C*-Algebras.}{http://www.utgjiu.ro/math/mbuneci/preprint/p0024.pdf},
{\em Surveys in Mathematics and its Applications}, Volume 1: 71--98.
\bibitem{AC79}
A. Connes.1979. Sur la th\'eorie noncommutative de l' integration, {\em Lecture Notes in
Math.}, Springer-Verlag, Berlin, {\bf 725}: 19-14. |
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Content:
{\bf \PMlinkescapetext{Definition} -} Let $X$ be a topological space and $\mathcal{B}$ be its \PMlinkname{Borel $\sigma$-algebra}{BorelSigmaAlgebra}. A {\bf Borel measure} on $X$ is a measure on the measurable space $(X,\mathcal{B})$.
{\bf Remark -} The \PMlinkname{restriction}{RestrictionOfAFunction} of the Lebesgue measure to the Borel $\sigma$-algebra of $\mathbb{R}^n$ is also sometimes called ``the'' Borel measure of $\mathbb{R}^n$. |
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