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measurable_space [2014/02/13 16:13] 127.0.0.1 external edit |
measurable_space [2014/06/25 10:20] nikolaj |
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| ===== Measurable space ===== | ===== Measurable space ===== | ||
| ==== Set ==== | ==== Set ==== | ||
| - | | @#88DDEE: $X $ | | + | | @#55CCEE: context | @#55CCEE: $ X $ | |
| - | + | | @#FFBB00: definiendum | @#FFBB00: $ \langle X,\Sigma\rangle\in \mathrm{MeasurableSpace}(X) $ | | |
| - | | @#55EE55: $ \langle X,\Sigma\rangle\in \mathrm{MeasurableSpace}(X) $ | | + | | @#55EE55: postulate | @#55EE55: $ \Sigma \in \mathrm{SigmaAlgebra}(X) $ | |
| - | + | ||
| - | | @#55EE55: $ \Sigma \in \mathrm{SigmaAlgebra}(X) $ | | + | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| Every σ-algebra gives us a measureable space. | Every σ-algebra gives us a measureable space. | ||
| + | |||
| + | === Predicates === | ||
| We call a set $X$ //measurable// if there is a sigma-algebra over it. | We call a set $X$ //measurable// if there is a sigma-algebra over it. | ||
