Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision Next revision | Previous revision | ||
smallest_generated_σ-algebra [2013/08/12 20:23] ben |
smallest_generated_σ-algebra [2013/08/18 14:48] nikolaj |
||
---|---|---|---|
Line 1: | Line 1: | ||
===== Smallest generated σ-algebra ===== | ===== Smallest generated σ-algebra ===== | ||
==== Definition ==== | ==== Definition ==== | ||
- | | @#88DDEE: $A\subseteq X$ | | + | | @#88DDEE: $X$ | |
- | | @#55EE55: $\sigma_X(A)\equiv \bigcap \{B\ |\ A\subseteq B\land B\subseteq \mathrm{SigmaAlgebra}(X)\} $ | | + | | @#55EE55: $\sigma(A):\equiv \bigcap \{C\ |\ A\subseteq C\land C\subseteq \mathrm{SigmaAlgebra}(X)\} $ | |
==== Discussion ==== | ==== Discussion ==== | ||
The smallest σ-algebra over $X$ generated by, and hence containing, $A$. | The smallest σ-algebra over $X$ generated by, and hence containing, $A$. |