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measure_space [2013/09/07 22:24] nikolaj |
measure_space [2016/06/20 18:31] nikolaj |
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| ===== Measure space ===== | ===== Measure space ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $X $ | | + | | @#55CCEE: context | @#55CCEE: $X $ | |
| - | + | | @#FFBB00: definiendum | @#FFBB00: $ \langle \langle X,\Sigma\rangle,\mu\rangle\in \mathrm{MeasureSpace}(X) $ | | |
| - | | @#FFBB00: $ \langle X,\Sigma,\mu\rangle\in \mathrm{MeasureSpace}(X) $ | | + | | @#55EE55: postulate | @#55EE55: $ \Sigma \in \mathrm{SigmaAlgebra}(X) $ | |
| - | + | | @#55EE55: postulate | @#55EE55: $ \mu\in \mathrm{Measure}(\Sigma) $ | | |
| - | | @#55EE55: $ \Sigma \in \mathrm{SigmaAlgebra}(X) $ | | + | |
| - | | @#55EE55: $ \mu\in \mathrm{Measure}(\Sigma) $ | | + | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| Line 15: | Line 13: | ||
| === Equivalent to === | === Equivalent to === | ||
| [[Measure]] | [[Measure]] | ||
| - | === Requirements === | + | === Context === |
| [[σ-algebra]], [[Extended real number line]], [[Infinite series]] | [[σ-algebra]], [[Extended real number line]], [[Infinite series]] | ||
