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σ-algebra [2016/06/20 18:43] nikolaj |
σ-algebra [2016/06/20 18:46] nikolaj |
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| ==== Set ==== | ==== Set ==== | ||
| | @#55CCEE: context | @#55CCEE: $X$ | | | @#55CCEE: context | @#55CCEE: $X$ | | ||
| - | | @#55EE55: postulate | @#55EE55: $ \Sigma\in \mathrm{SigmaAlgebra}(X) $ | | + | | @#FFBB00: definiendum | @#FFBB00: $\Sigma$ in it | |
| | @#55EE55: postulate | @#55EE55: $\Sigma\subseteq \mathcal P(X)$ | | | @#55EE55: postulate | @#55EE55: $\Sigma\subseteq \mathcal P(X)$ | | ||
| | @#55EE55: postulate | @#55EE55: $ \Sigma\ne\emptyset $ | | | @#55EE55: postulate | @#55EE55: $ \Sigma\ne\emptyset $ | | ||
| - | | @#55CCEE: context | @#55CCEE: $E\in\Sigma$ | | + | | forall | $E\in\Sigma$ | |
| - | | $A\in\mathrm{Sequence}(\Sigma)$ | | + | |
| - | | @#DDDDDD: range | @#DDDDDD: $n\in \mathbb N$ | | + | |
| | @#55EE55: postulate | @#55EE55: $ X\smallsetminus E \in \Sigma $ | | | @#55EE55: postulate | @#55EE55: $ X\smallsetminus E \in \Sigma $ | | ||
| + | | forall | $A\in\mathrm{Sequence}(\Sigma)$ | | ||
| + | | forall | $n\in \mathbb N$ | | ||
| | @#55EE55: postulate | @#55EE55: $ \bigcup_{i=1}^n A_i \in \Sigma $ | | | @#55EE55: postulate | @#55EE55: $ \bigcup_{i=1}^n A_i \in \Sigma $ | | ||
