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measure_space [2013/09/06 23:11] nikolaj |
measure_space [2014/03/21 11:11] 127.0.0.1 external edit |
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| ===== Measure space ===== | ===== Measure space ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $X $ | | + | | @#55CCEE: context | @#55CCEE: $X $ | |
| - | | @#55EE55: $ \langle X,\Sigma,\mu\rangle\in \mathrm{MeasureSpace}(X) $ | | + | | @#FFBB00: definiendum | @#FFBB00: $ \langle X,\Sigma,\mu\rangle\in \mathrm{MeasureSpace}(X) $ | |
| - | | @#55EE55: $ \Sigma \in \mathrm{SigmaAlgebra}(X) $ | | + | | @#55EE55: postulate | @#55EE55: $ \Sigma \in \mathrm{SigmaAlgebra}(X) $ | |
| - | | @#55EE55: $ \mu\in \mathrm{Measure}(\Sigma) $ | | + | | @#55EE55: postulate | @#55EE55: $ \mu\in \mathrm{Measure}(\Sigma) $ | |
| - | ==== Ramifications ==== | + | ==== Discussion ==== |
| A measure space is a measurable space together with a fixed measure. | A measure space is a measurable space together with a fixed measure. | ||
| ==== Reference ==== | ==== Reference ==== | ||
| Line 15: | Line 15: | ||
| === Equivalent to === | === Equivalent to === | ||
| [[Measure]] | [[Measure]] | ||
| - | === Requirements === | + | === Context === |
| [[σ-algebra]], [[Extended real number line]], [[Infinite series]] | [[σ-algebra]], [[Extended real number line]], [[Infinite series]] | ||
