Talk:Measure (mathematics): Difference between revisions
imported>Aleksander Halicz (remarks) |
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* application - it would be nice to mention that some basic probability theory may be viewed as a direct application of the measure theory (identifying basic correspondence, definition of probability, types of convergence etc) | * application - it would be nice to mention that some basic probability theory may be viewed as a direct application of the measure theory (identifying basic correspondence, definition of probability, types of convergence etc) | ||
[[User:Aleksander Halicz|Aleksander Halicz]] 03:38, 7 February 2007 (CST) | [[User:Aleksander Halicz|Aleksander Halicz]] 03:38, 7 February 2007 (CST) | ||
You write | |||
This does for instance happen in the real line case, where one expects any "natural" measure to be translation invariant. For such a measure there exists a set, which, if measurable, permits a direct proof of self-contradictory consequences, such as finite upper bound for an infinite sum of positive elements. | |||
It might be that I don't follow your presentation, but are you thinking of a specific example. Of itself, such an infinite sum shouldn't pose a problem (i.e. sum of 1/2^n), so I think I'm missing something. | |||
On a related note, I wonder how much we should include in the introductory section before a section of ''motivation'' is warranted. Still, I'm not certain if that's the most important thing right now. | |||
[[User:Simen Rustad|Simen Rustad]] 15:52, 8 February 2007 (CST) | |||
Revision as of 15:52, 8 February 2007
It is really enjoyable for a non mathematiciation to see this here, and easy to read too David Tribe 16:27, 25 January 2007 (CST)
remarks
Just a few thoughts to remember (how to reorganize this)
- separate particular examples from general classes (now Dirac measure is at the same logical level as Borel or Radon measure)
- sigma-finite and completeness are more or less at the same logical level (classes of measures)
- counterexamples should be moved to the lead to give some motivation or explication for the need of the sigma-algebras.
- application - it would be nice to mention that some basic probability theory may be viewed as a direct application of the measure theory (identifying basic correspondence, definition of probability, types of convergence etc)
Aleksander Halicz 03:38, 7 February 2007 (CST)
You write
This does for instance happen in the real line case, where one expects any "natural" measure to be translation invariant. For such a measure there exists a set, which, if measurable, permits a direct proof of self-contradictory consequences, such as finite upper bound for an infinite sum of positive elements.
It might be that I don't follow your presentation, but are you thinking of a specific example. Of itself, such an infinite sum shouldn't pose a problem (i.e. sum of 1/2^n), so I think I'm missing something.
On a related note, I wonder how much we should include in the introductory section before a section of motivation is warranted. Still, I'm not certain if that's the most important thing right now.
Simen Rustad 15:52, 8 February 2007 (CST)