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smallest_generated_σ-algebra [2013/08/18 14:45] nikolaj |
smallest_generated_σ-algebra [2014/03/21 11:11] |
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| - | ===== Smallest generated σ-algebra ===== | ||
| - | ==== Definition ==== | ||
| - | | @#88DDEE: $X$ | | ||
| - | | @#55EE55: $\sigma_X(A):\equiv \bigcap \{C\ |\ A\subseteq C\land C\subseteq \mathrm{SigmaAlgebra}(X)\} $ | | ||
| - | ==== Discussion ==== | ||
| - | The smallest σ-algebra over $X$ generated by, and hence containing, $A$. | ||
| - | |||
| - | ==== Reference ==== | ||
| - | Wikipedia: [[http://de.wikipedia.org/wiki/%CE%A3-Algebra#Bedeutung|σ-Operator (german)]] | ||
| - | ==== Context ==== | ||
| - | === Element of === | ||
| - | [[σ-algebra]] | ||
