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complete_measure_space [2013/09/07 23:22] nikolaj created |
complete_measure_space [2014/03/21 11:11] |
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| - | ===== Measure space ===== | ||
| - | ==== Definition ==== | ||
| - | | @#88DDEE: $X $ | | ||
| - | | @#FFBB00: $ \langle X,\Sigma,\mu\rangle $ ... complete measure space over $X$ | | ||
| - | |||
| - | | @#55EE55: $ \langle X,\Sigma,\mu\rangle $ ... measure space | | ||
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| - | | $\mu(N)=0$ | | ||
| - | | $N'\subseteq N $ | | ||
| - | |||
| - | | @#55EE55: $ N'\in\Sigma $ | | ||
| - | |||
| - | ==== Discussion ==== | ||
| - | In a complete measure space, subsets of null-sets can also be measured (and they then have zero measure as well). This notion is just introduced to prevent some pathologies. | ||
| - | ==== Reference ==== | ||
| - | Wikipedia: [[http://en.wikipedia.org/wiki/Complete_measure|Complete measure]] | ||
| - | ==== Parents ==== | ||
| - | === Subset of === | ||
| - | [[Measure space]] | ||
