Timeline for Is there a "disjoint union" sigma algebra?
Current License: CC BY-SA 2.5
7 events
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| Dec 4, 2019 at 9:41 | comment | added | Robert Furber | @Jeff The reason your definition is not more commonly used is that it is not a coproduct in the category of measurable spaces, for exactly the reason you give (you can't patch together measurable functions and form the dotted arrow in the diagram that defines a categorical coproduct). I could also add that in my experience, the countable-cocountable algebra is only useful for making counterexamples, rather than in applications of measure theory. | |
| May 20, 2014 at 21:14 | comment | added | Jeff | Mine has the unfortunate consequence that you cannot piece together measurable functions from each piece, but you normally can't do that anyway. | |
| May 20, 2014 at 21:14 | comment | added | Jeff | @PeterLeFanuLumsdaine Do you know why this construction you mention is more commonly used than another reasonable seeming alternative: The sigma algebra generated by the measurable sets of each of the $A_i$ This would sort of parallel the "countable cocountable" construction as opposed to yours which is the analog of "power set." More rigorously, your disjoint union of uncountably many 1 point spaces would give power set sigma algebra, but mine would give countable cocountable. | |
| Apr 5, 2011 at 17:02 | history | edited | Peter LeFanu Lumsdaine | CC BY-SA 2.5 |
correction as pointed out in comments
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| Feb 11, 2011 at 1:35 | history | edited | Peter LeFanu Lumsdaine | CC BY-SA 2.5 |
added accidentally omitted word
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| Feb 10, 2011 at 14:50 | vote | accept | Neil Toronto | ||
| Feb 9, 2011 at 20:48 | history | answered | Peter LeFanu Lumsdaine | CC BY-SA 2.5 |