Timeline for Modified Lebesgue differentiation theorem
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Nov 20, 2011 at 20:08 | answer | added | Florian | timeline score: 4 | |
| Oct 19, 2011 at 17:05 | comment | added | Pietro Majer | To sketch the standard argument: Since countable intersections of full-measure sets is a full-measure set, a countable set of integrable functions admits a common full-measure set $S\subset\Omega$ of differentiation (that is, such that the first formula you wrote holds for every function of the family and for every $x\in S$). Consider in particular the functions $u_q(y):=|u(y)-q|$, $q$ a rational number. Then it is easy to see that for all $x\in S$ the second formula you wrote is true. Check for instance Wheeden- Zygmund, Measure and integral. | |
| Oct 19, 2011 at 14:12 | comment | added | Gerald Edgar | Such a point is called a "Lebesgue point" of $u$. Look for that in your textbook. Here it is in Wikipedia: en.wikipedia.org/wiki/Lebesgue_point | |
| Oct 19, 2011 at 13:30 | history | asked | Florian | CC BY-SA 3.0 |