Locally finite measure - Revision history

en>Yobot: /* Definition */WP:CHECKWIKI error fixes using AWB (10093)

2014-05-05T12:09:18Z

Definition: WP:CHECKWIKI error fixes using AWB (10093)

← Older revision		Revision as of 14:09, 5 May 2014
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	~~In [[linear algebra]], [[functional analysis]] and related areas of [[mathematics]], a '''quasinorm''~~' is ~~similar~~ to ~~a [[Norm (mathematics)\|norm]] in that~~ it ~~satisfies the norm axioms, except that the [~~[~~triangle inequality]] is replaced by~~		I'm Luther but I by no auto warranty means truly liked that title. The factor she adores most is to perform handball but she can't make it her profession. Managing individuals is how [http://89.1.13.189/index.php?mod=users&action=view&id=63366 car warranty] she makes cash and she will not alter it anytime [http://www.nanumgdc.com/forest/board_xUbo69/841259 extended car warranty] auto warranty soon. [http://Www.Continentalwarranty.org/ Delaware] is the place [http://Extended-car-warranty-services-review.toptenreviews.com/ I adore] most but I require to move for my family members.<br><br>Look into my site [http://www.caribbeansocialnetwork.com/groups/easy-diy-repair-strategies-for-your-automobile/ extended car warranty]
	:~~<math>\\|x + y\\| \leq K(\\|x\\| + \\|y\\|)<~~/~~math>~~
	~~for some <math>K >~~ 1.</~~math>~~

	~~This is not to be confused with a '''[[seminorm]]''' or '''[[pseudonorm]]''', where the norm axioms are satisfied except for positive definiteness~~.

	== ~~Related concepts~~ ==
	A [~~[vector space]~~] ~~with an associated quasinorm is called a '''quasinormed vector space'''~~.

	A [~~[complete space\|complete]] quasinormed vector space is called a '''quasi-Banach space'''~~.

	~~A quasinormed space <math>(A, \\| \cdot \\|)<~~/~~math>~~ is ~~called a '''quasinormed algebra''' if~~ the ~~vector space ''A'' is an [~~[~~Algebra over a field\|algebra]] and there is a constant ''K'' > 0 such that~~
	:~~<math>\\|xy\\| \leq K \\|x\\| \cdot \\|y\\|<~~/~~math>~~
	~~for all <math>x, y \in A<~~/~~math>.~~

	~~A complete quasinormed algebra is called a '''quasi~~-~~Banach algebra'''.~~

	~~== See also ==~~
	*[[Seminorm]]

	~~== References ==~~

	* {{cite book \| title=Handbook of the History of General Topology \| last=Aull \| first=Charles E. \| coauthors=Robert Lowen \| year=2001 \| isbn=0-~~7923~~-~~6970~~-~~X \| publisher=[[Springer Science+Business Media\|Springer]] }}~~
	* {{cite book \| title=A Course in Functional Analysis \| last=Conway \| first=John B. ~~\| isbn=0-387-97245-5 \| publisher=[[Springer Science+Business Media\|Springer]~~] ~~\| year=1990 }}~~
	* {{cite book \| title=Functional Analysis I: Linear Functional Analysis \| last=Nikolʹskiĭ \| first=Nikolaĭ Kapitonovich \| isbn=3-540-50584-9 \| year=1992 \| publisher=[[Springer Science+Business Media\|Springer]] \| series=Encyclopaedia of Mathematical Sciences \| volume=19 }}
	* {{cite book \| title=An Introduction to ~~Functional Analysis \| last=Swartz \| first=Charles \| year=1992 \| publisher=~~[~~[CRC Press]] \| isbn=0~~-~~8247~~-~~8643~~-~~2 }}~~

	<!--~~Categories~~-->
	~~[[Category:Norms (mathematics)]]~~
	~~[[Category:Linear algebra]~~]

en>Aetheling: /* Definition */ add link

2013-08-06T14:48:11Z

Definition: add link

← Older revision		Revision as of 16:48, 6 August 2013
Line 1:		Line 1:
	~~The name~~ of the ~~author~~ is ~~Garland~~. ~~To keep birds~~ is ~~one of~~ the ~~things he enjoys most~~. ~~Her spouse and her selected to reside in Alabama~~. ~~Interviewing~~ is ~~what she does in her working day occupation but soon her husband and her will begin their own company~~.<br><br>~~My web-site~~ [~~http~~://~~www~~.~~pietreta~~.~~com/UserProfile/tabid/42/userId/8740/language/en~~-~~US/Default~~.~~aspx car warranty companies~~]		In [[linear algebra]], [[functional analysis]] and related areas of [[mathematics]], a '''quasinorm''' is similar to a [[Norm (mathematics)\|norm]] in that it satisfies the norm axioms, except that the [[triangle inequality]] is replaced by
			:<math>\\|x + y\\| \leq K(\\|x\\| + \\|y\\|)</math>
			for some <math>K > 1.</math>

			This is not to be confused with a '''[[seminorm]]''' or '''[[pseudonorm]]''', where the norm axioms are satisfied except for positive definiteness.

			== Related concepts ==
			A [[vector space]] with an associated quasinorm is called a '''quasinormed vector space'''.

			A [[complete space\|complete]] quasinormed vector space is called a '''quasi-Banach space'''.

			A quasinormed space <math>(A, \\| \cdot \\|)</math> is called a '''quasinormed algebra''' if the vector space ''A'' is an [[Algebra over a field\|algebra]] and there is a constant ''K'' > 0 such that
			:<math>\\|xy\\| \leq K \\|x\\| \cdot \\|y\\|</math>
			for all <math>x, y \in A</math>.

			A complete quasinormed algebra is called a '''quasi-Banach algebra'''.

			== See also ==
			*[[Seminorm]]

			== References ==

			* {{cite book \| title=Handbook of the History of General Topology \| last=Aull \| first=Charles E. \| coauthors=Robert Lowen \| year=2001 \| isbn=0-7923-6970-X \| publisher=[[Springer Science+Business Media\|Springer]] }}
			* {{cite book \| title=A Course in Functional Analysis \| last=Conway \| first=John B. \| isbn=0-387-97245-5 \| publisher=[[Springer Science+Business Media\|Springer]] \| year=1990 }}
			* {{cite book \| title=Functional Analysis I: Linear Functional Analysis \| last=Nikolʹskiĭ \| first=Nikolaĭ Kapitonovich \| isbn=3-540-50584-9 \| year=1992 \| publisher=[[Springer Science+Business Media\|Springer]] \| series=Encyclopaedia of Mathematical Sciences \| volume=19 }}
			* {{cite book \| title=An Introduction to Functional Analysis \| last=Swartz \| first=Charles \| year=1992 \| publisher=[[CRC Press]] \| isbn=0-8247-8643-2 }}

			<!--Categories-->
			[[Category:Norms (mathematics)]]
			[[Category:Linear algebra]]

en>French Tourist: copy-paste error while adding an interwiki !

2012-02-05T21:36:32Z

copy-paste error while adding an interwiki !

New page

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