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Maharam algebra : ウィキペディア英語版
Maharam algebra
In mathematics, a Maharam algebra is a complete Boolean algebra with a continuous submeasure. They were introduced by .
==Definitions==

A continuous submeasure or Maharam submeasure on a Boolean algebra is a real-valued function ''m'' such that
* ''m''(0) = 0, ''m''(1) = 1, ''m''(''x'') > 0 if ''x'' ≠ 0.
* If ''x'' < ''y'' then ''m''(''x'') < ''m''(''y'')
* ''m''(''x'' ∨ ''y'') ≤ ''m''(''x'') + ''m''(''y'')
* If ''x''''n'' is a decreasing sequence with intersection 0, then the sequence ''m''(''x''''n'') has limit 0.
A Maharam algebra is a complete Boolean algebra with a continuous submeasure.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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