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measure_space [2013/09/06 23:11] nikolaj |
measure_space [2016/06/20 18:37] nikolaj |
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===== Measure space ===== | ===== Measure space ===== | ||
- | ==== Definition ==== | + | ==== Set ==== |
- | | @#88DDEE: $X $ | | + | | @#55CCEE: context | @#55CCEE: $X $ | |
+ | | @#FFBB00: definiendum | @#FFBB00: $ \langle\!\langle X,\Sigma,\mu \rangle\!\rangle$ in it | | ||
+ | | @#55EE55: postulate | @#55EE55: $ \Sigma \in \mathrm{SigmaAlgebra}(X) $ | | ||
+ | | @#55EE55: postulate | @#55EE55: $ \mu\in \mathrm{Measure}(\Sigma) $ | | ||
- | | @#55EE55: $ \langle X,\Sigma,\mu\rangle\in \mathrm{MeasureSpace}(X) $ | | + | ==== Discussion ==== |
- | + | ||
- | | @#55EE55: $ \Sigma \in \mathrm{SigmaAlgebra}(X) $ | | + | |
- | | @#55EE55: $ \mu\in \mathrm{Measure}(\Sigma) $ | | + | |
- | + | ||
- | ==== Ramifications ==== | + | |
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 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]] | ||