Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision Last revision Both sides next revision | ||
|
measure [2015/04/01 10:29] nikolaj |
measure [2015/04/01 10:30] nikolaj |
||
|---|---|---|---|
| Line 5: | Line 5: | ||
| | @#55CCEE: context | @#55CCEE: $E\in \Sigma$ | | | @#55CCEE: context | @#55CCEE: $E\in \Sigma$ | | ||
| | @#55CCEE: context | @#55CCEE: $S\in \mathrm{Sequence}(\Sigma)$ | | | @#55CCEE: context | @#55CCEE: $S\in \mathrm{Sequence}(\Sigma)$ | | ||
| - | | @#55EE55: postulate | @#55EE55: $ \mu:\Sigma\to \overline{\mathbb R} $ | | + | | @#AAFFAA: inclusion | @#AAFFAA: \mu:\Sigma\to \overline{\mathbb R} $ | |
| - | | @#55EE55: postulate | @#55EE55: $ \mu(\emptyset)=0 $ | | + | |
| | @#55EE55: postulate | @#55EE55: $ \mu(E)\ge 0$ | | | @#55EE55: postulate | @#55EE55: $ \mu(E)\ge 0$ | | ||
| + | | @#55EE55: postulate | @#55EE55: $ \mu(\emptyset)=0 $ | | ||
| | @#55EE55: postulate | @#55EE55: $ \mu\left(\bigcup_{j=1}^\infty S_j\right)=\sum_{j=1}^\infty \mu(S_j) $ | | | @#55EE55: postulate | @#55EE55: $ \mu\left(\bigcup_{j=1}^\infty S_j\right)=\sum_{j=1}^\infty \mu(S_j) $ | | ||
| Line 15: | Line 15: | ||
| ----- | ----- | ||
| - | === Equivalent to === | ||
| - | [[Measure space]] | ||
| === Context === | === Context === | ||
| [[σ-algebra]], [[Extended real number line]], [[Infinite series]] | [[σ-algebra]], [[Extended real number line]], [[Infinite series]] | ||
| + | |||
| + | === Equivalent to === | ||
| + | [[Measure space]] | ||
