Maximal arc - Revision history

en>Rjwilmsi: /* References */Added 4 dois to journal cites using AWB (10209)

2014-05-24T08:19:55Z

References: Added 4 dois to journal cites using AWB (10209)

← Older revision		Revision as of 10:19, 24 May 2014
Line 1:		Line 1:
	~~In [[mathematics]], a function ''f'' on~~ the ~~interval [''a'', ''b''] has~~ the '~~''Luzin N property''', named after [[Nikolai Luzin]] (also called Luzin property or N property) if for all~~ <~~math~~>~~N\subset[a,b]~~<~~/math~~> ~~such that <math>\lambda(N)=0</math>, there holds~~: ~~<math>\lambda(f(N))=0<~~/~~math>, where <math>\lambda<~~/~~math> stands for the [[Lebesgue measure]]~~.		The name of the writer is Garland. Delaware is the only location I've been residing in. To perform badminton is something he truly enjoys doing. Managing people is what I do in my day job.<br><br>Here is my web site [http://www.clan-myreality.de/index.php?mod=users&action=view&id=9712 http://www.clan-myreality.de]

	Note that the image of such a set ''N'' is not necessarily [[measurable set\|measurable]], but since the Lebesgue measure is [[Complete measure\|complete]], it follows that if the Lebesgue [[outer measure]] of that set is zero, then it is measurable and its Lebesgue measure is zero as well.

	~~==Properties==~~
	~~Every [[absolutely continuous]] function has the Luzin N property~~. ~~The [[Cantor function]] on the other hand does not: the Lebesgue measure of the [[Cantor set]] is zero, however its image is the complete [0,1] interval.~~

	~~Also, if a function ''f'' on the interval [''a'',''b''] is [[continuous function\|continuous]], is of [[bounded variation]] and has the Luzin N property, then it is [[absolutely continuous]].~~

	==~~External links~~==
	*[http://~~eom~~.~~springer~~.de~~/L/l061050.htm Springer Online~~]

	~~[[Category:Real analysis]]~~
	~~[[Category:Measure theory]]~~

	~~{{mathanalysis-stub}}~~

en>Wcherowi: /* Properties */ clarification

2012-11-25T17:23:26Z

Properties: clarification

← Older revision		Revision as of 19:23, 25 November 2012
Line 1:		Line 1:
	~~The author~~ is ~~known~~ as ~~Irwin~~. ~~Years in~~ the ~~past he moved to North Dakota and his family enjoys it~~. ~~Hiring~~ is ~~my occupation~~. ~~One of~~ the ~~things she loves most~~ is ~~to read comics~~ and ~~she'll be starting something else along with~~ it.~~<br><br>Also visit my weblog ... std testing at home [~~[http://~~203~~.~~250~~.~~78.160~~/~~zbxe~~/~~?document_srl=810524&mid=gallery&sort_index=regdate&order_type=desc click here for more~~]]		In [[mathematics]], a function ''f'' on the interval [''a'', ''b''] has the '''Luzin N property''', named after [[Nikolai Luzin]] (also called Luzin property or N property) if for all <math>N\subset[a,b]</math> such that <math>\lambda(N)=0</math>, there holds: <math>\lambda(f(N))=0</math>, where <math>\lambda</math> stands for the [[Lebesgue measure]].

			Note that the image of such a set ''N'' is not necessarily [[measurable set\|measurable]], but since the Lebesgue measure is [[Complete measure\|complete]], it follows that if the Lebesgue [[outer measure]] of that set is zero, then it is measurable and its Lebesgue measure is zero as well.

			==Properties==
			Every [[absolutely continuous]] function has the Luzin N property. The [[Cantor function]] on the other hand does not: the Lebesgue measure of the [[Cantor set]] is zero, however its image is the complete [0,1] interval.

			Also, if a function ''f'' on the interval [''a'',''b''] is [[continuous function\|continuous]], is of [[bounded variation]] and has the Luzin N property, then it is [[absolutely continuous]].

			==External links==
			*[http://eom.springer.de/L/l061050.htm Springer Online]

			[[Category:Real analysis]]
			[[Category:Measure theory]]

			{{mathanalysis-stub}}

en>FrescoBot: Bot: fixing section wikilinks

2012-07-06T03:01:53Z

Bot: fixing section wikilinks

New page

The author is known as Irwin. Years in the past he moved to North Dakota and his family enjoys it. Hiring is my occupation. One of the things she loves most is to read comics and she'll be starting something else along with it.<br><br>Also visit my weblog ... std testing at home [[http://203.250.78.160/zbxe/?document_srl=810524&mid=gallery&sort_index=regdate&order_type=desc click here for more]]