| 21. | See non-measurable set for more details.
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| 22. | Whenever " A " and " B " are any measurable sets and ? is the associated measure.
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| 23. | The ?-measurable sets form a ?-algebra and ? restricted to the measurable sets is a countably additive complete measure.
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| 24. | The ?-measurable sets form a ?-algebra and ? restricted to the measurable sets is a countably additive complete measure.
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| 25. | Halmos ) as a measurable set of positive measure that has no subsets of strictly less, yet positive measure.
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| 26. | Show that the set of points for which \ { f _ n \ } converges is a measurable set.
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| 27. | Specifically, this is true if the measure space contains an infinite family of disjoint measurable sets of finite positive measure.
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| 28. | A function between two measurable spaces is called a measurable function if the preimage of every measurable set is measurable.
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| 29. | In ZF, one can show that the Hahn Banach theorem is enough to derive the existence of a non-Lebesgue measurable set.
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| 30. | A measure is called " ?-finite " if can be decomposed into a countable union of measurable sets of finite measure.
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