Constant-weight code - Revision history

en>DavidCary: /* Balanced code */ yet another balanced code

2015-01-12T17:17:48Z

Balanced code: yet another balanced code

← Older revision		Revision as of 19:17, 12 January 2015
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	~~In [[mathematics]], a nonempty collection~~ of ~~[[Set (mathematics)\|sets]] <math>\mathcal{R}</math>~~ is ~~called a~~ '~~''δ-ring''' (pronounced ''delta-ring'') if~~ it is ~~[[closure (mathematics)\|closed]] under [[union (set theory)\|union]], [[Complement (set theory)\|relative complementation]], and countable [[Intersection (set theory)\|intersection]]:~~		The name of the author is Jayson. North Carolina is the place he enjoys most but now he is contemplating other choices. The preferred pastime for him and his children is style and he'll be starting some thing else alongside with it. He is an information officer.<br><br>my web blog; best psychic ([http://www.zavodpm.ru/blogs/glennmusserrvji/14565-great-hobby-advice-assist-allow-you-get-going click here])
	#<~~math~~>~~A \cup B \in \mathcal{R}~~<~~/math~~> ~~if <math>A, B \in \mathcal{R}</math>~~
	~~#<math>A - B \in \mathcal{R}<~~/~~math> if <math>A, B \in \mathcal{R}<~~/~~math>~~
	~~#<math>\bigcap_{n=1}^{\infty} A_{n} \in \mathcal{R}<~~/~~math> if <math>A_{n} \in \mathcal{R}<~~/~~math> for all <math>n \in \mathbb{N}<~~/~~math>~~

	~~If only the first two properties are satisfied, then <math>\mathcal{R}</math> is a [[Ring of sets\|ring]] but not a δ~~-~~ring. Every [[Sigma~~-~~ring\|σ~~-~~ring]] is a δ~~-~~ring, but not every δ~~-~~ring is a σ-ring.~~

	δ-~~rings can be used instead of [[Sigma~~-~~algebra\|σ~~-~~fields~~]~~] in the development of [[Measure (mathematics~~)~~\|measure]] theory if one does not wish to allow sets of infinite measure.~~

	~~== See also ==~~
	*[[Ring of sets]]
	*[[Sigma-algebra\|Sigma field]]
	*[[Sigma ring]]

	~~== References ==~~
	* Cortzen, Allan. "Delta-Ring." From MathWorld—A Wolfram Web Resource, created by Eric W. Weisstein. http://mathworld.wolfram.com/Delta-Ring.html

	~~{{Mathanalysis-stub}}~~

	~~[[Category:Measure theory]]~~
	~~[[Category:Set families]]~~

en>Atethnekos: fix cs1 error

2013-11-29T07:42:03Z

fix cs1 error

← Older revision		Revision as of 09:42, 29 November 2013
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	~~I would like to introduce myself to you~~, ~~I am Andrew and my wife doesn~~'~~t like~~ it at all. ~~Distributing production~~ is ~~how he makes~~ a ~~living~~. ~~To climb is something she would~~ [http://~~www~~.~~khuplaza~~.com/~~dent/14869889 psychic solutions by lynne~~] ~~no means give up. My spouse and I reside in Mississippi and I adore every working day living here.~~		In [[mathematics]], a nonempty collection of [[Set (mathematics)\|sets]] <math>\mathcal{R}</math> is called a '''δ-ring''' (pronounced ''delta-ring'') if it is [[closure (mathematics)\|closed]] under [[union (set theory)\|union]], [[Complement (set theory)\|relative complementation]], and countable [[Intersection (set theory)\|intersection]]:
			#<math>A \cup B \in \mathcal{R}</math> if <math>A, B \in \mathcal{R}</math>
			#<math>A - B \in \mathcal{R}</math> if <math>A, B \in \mathcal{R}</math>
			#<math>\bigcap_{n=1}^{\infty} A_{n} \in \mathcal{R}</math> if <math>A_{n} \in \mathcal{R}</math> for all <math>n \in \mathbb{N}</math>

			If only the first two properties are satisfied, then <math>\mathcal{R}</math> is a [[Ring of sets\|ring]] but not a δ-ring. Every [[Sigma-ring\|σ-ring]] is a δ-ring, but not every δ-ring is a σ-ring.

			δ-rings can be used instead of [[Sigma-algebra\|σ-fields]] in the development of [[Measure (mathematics)\|measure]] theory if one does not wish to allow sets of infinite measure.

			== See also ==
			*[[Ring of sets]]
			*[[Sigma-algebra\|Sigma field]]
			*[[Sigma ring]]

			== References ==
			* Cortzen, Allan. "Delta-Ring." From MathWorld—A Wolfram Web Resource, created by Eric W. Weisstein. http://mathworld.wolfram.com/Delta-Ring.html

			{{Mathanalysis-stub}}

			[[Category:Measure theory]]
			[[Category:Set families]]

en>AnomieBOT: Dating maintenance tags: {{Mergefrom}}

2012-04-28T05:53:34Z

Dating maintenance tags: {{Mergefrom}}

New page

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