| Version 10 |
Version 9 |
| \begin{definition} |
\begin{definition} |
|
A {\em Borel space} $(X; \mathcal{B}(X))$ is defined as a set $X$, together with
|
A {\em Borel space} $(X; \mathcal{B}(X))$ is defined as a \emph{topological space $X$, together with
|
| a \PMlinkname{$\sigma$-algebra}{SigmaAlgebra} $\mathcal{B}(X)$ of subsets of $X$, called Borel sets}. |
a \PMlinkname{$\sigma$-algebra}{SigmaAlgebra} $\mathcal{B}(X)$ of subsets of $X$, called Borel sets}. |
| \end{definition} |
\end{definition} |
|
|
| \textbf{Note} |
\textbf{Note} |
| A subspace of a Borel space $(X; \mathcal{B} (X))$ is a subset $S \subset X$ endowed with the relative Borel structure, |
A subspace of a Borel space $(X; \mathcal{B} (X))$ is a subset $S \subset X$ endowed with the relative Borel structure, |
| that is the $\sigma$-algebra of all subsets of $S$ of the form $S \bigcap E$, where $E$ is a Borel subset of $X$. |
that is the $\sigma$-algebra of all subsets of $S$ of the form $S \bigcap E$, where $E$ is a Borel subset of $X$. |
|
|
|
|
|
|
|
|
| \begin{thebibliography}{9} |
\begin{thebibliography}{9} |
|
|
| \bibitem{MRB2k6} |
\bibitem{MRB2k6} |
| M.R. Buneci. 2006., |
M.R. Buneci. 2006., |
| \PMlinkexternal{Groupoid C*-Algebras.}{http://www.utgjiu.ro/math/mbuneci/preprint/p0024.pdf}, |
\PMlinkexternal{Groupoid C*-Algebras.}{http://www.utgjiu.ro/math/mbuneci/preprint/p0024.pdf}, |
| {\em Surveys in Mathematics and its Applications}, Volume 1: 71--98. |
{\em Surveys in Mathematics and its Applications}, Volume 1: 71--98. |
|
|
| \bibitem{AC79} |
\bibitem{AC79} |
| A. Connes.1979. Sur la th\'eorie noncommutative de l' integration, {\em Lecture Notes in |
A. Connes.1979. Sur la th\'eorie noncommutative de l' integration, {\em Lecture Notes in |
| Math.}, Springer-Verlag, Berlin, {\bf 725}: 19-14. |
Math.}, Springer-Verlag, Berlin, {\bf 725}: 19-14. |
|
|
| \end{thebibliography} |
\end{thebibliography} |
