Daniell integral: Difference between revisions
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The construction of the [[Lebesgue integral]] is built on top of [[measure theory]]. Another approach that could be used to generalize [[Riemann integral|Riemann's Integral]] is to do so by using some sort of extension process, thereby avoiding the need for measure theory. This was the approach taken by [[Percy Daniell]] (and later generalized by [[Marshall Stone]]). |
The construction of the [[Lebesgue integral]] is built on top of [[measure theory]]. Another approach that could be used to generalize [[Riemann integral|Riemann's Integral]] is to do so by using some sort of extension process, thereby avoiding the need for measure theory. This was the approach taken by [[Percy Daniell]] (and later generalized by [[Marshall Stone]]). |
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Everything2 has a nice writeup on this topic which can be found [http://www.everything2.com/index.pl?node_id=1520588 here]. |
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== Further Reading == |
== Further Reading == |
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Revision as of 06:00, 1 April 2006
The construction of the Lebesgue integral is built on top of measure theory. Another approach that could be used to generalize Riemann's Integral is to do so by using some sort of extension process, thereby avoiding the need for measure theory. This was the approach taken by Percy Daniell (and later generalized by Marshall Stone).
Further Reading
- H. L. Royden, Real Analysis, Third Edition, Prentice Hall, 1988.
- http://www.probabilityandfinance.com/articles/04.pdf
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