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- mathematischer Satz (de)
- theorem (en)
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- Let be a -system that contains and let be a collection of functions from to with the following properties:
# If then where denotes the indicator function of
# If and then and
# If is a sequence of non-negative functions that increase to a bounded function then
Then contains all bounded functions that are measurable with respect to which is the -algebra generated by (en)
- Let be an algebra of sets and define to be the smallest monotone class containing Then is precisely the -algebra generated by ; that is (en)
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- Monotone class theorem for functions (en)
- Monotone class theorem for sets (en)
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- The assumption , and imply that is a -system.
By and the − theorem,
Statement implies that contains all simple functions, and then implies that contains all bounded functions measurable with respect to (en)
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- Monotone class theorem (en)
- Satz über monotone Klassen (de)
- Теорема про монотонний клас (uk)
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