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smallest_generated_σ-algebra [2013/08/18 14:48] nikolaj |
smallest_generated_σ-algebra [2014/03/21 11:11] (current) |
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===== Smallest generated σ-algebra ===== | ===== Smallest generated σ-algebra ===== | ||
- | ==== Definition ==== | + | ==== Set ==== |
- | | @#88DDEE: $X$ | | + | | @#55CCEE: context | @#55CCEE: $X$ | |
- | | @#55EE55: $\sigma(A):\equiv \bigcap \{C\ |\ A\subseteq C\land C\subseteq \mathrm{SigmaAlgebra}(X)\} $ | | + | | @#55EE55: postulate | @#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, $A$. | ||
Line 9: | Line 9: | ||
==== Reference ==== | ==== Reference ==== | ||
Wikipedia: [[http://de.wikipedia.org/wiki/%CE%A3-Algebra#Bedeutung|σ-Operator (german)]] | Wikipedia: [[http://de.wikipedia.org/wiki/%CE%A3-Algebra#Bedeutung|σ-Operator (german)]] | ||
- | ==== Context ==== | + | ==== Parents ==== |
=== Element of === | === Element of === | ||
[[σ-algebra]] | [[σ-algebra]] |