en>BD2412: minor fixes, mostly disambig links using AWB

2014-10-03T16:07:43Z

minor fixes, mostly disambig links using AWB

← Older revision		Revision as of 18:07, 3 October 2014
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	~~{{distinguish\|Cartan's theorem}}~~
	In [[potential theory]], a branch of [[mathematics]], '''Cartan's lemma''', named after [[Henri Cartan]], is a bound on the measure and complexity of the set on which a logarithmic [[Newtonian potential]] is small. The following statement can be found in Levin's book.<ref>B.Ya. Levin, ''Lectures on Entire Functions''</ref>

	~~Let ''μ'' be a finite positive [[Borel measure]] on the complex plane '''C''' with ''μ''('''C''') = ''n''. Let ''u''(''z'') be the logarithmic potential of ''μ'':~~

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	~~Given ''H'' ∈ (0~~,&~~nbsp~~;1), ~~there exist discs~~ of ~~radius ''r''~~<~~sub~~>~~''i''~~<~~/sub~~> such that

	:<~~math~~>~~\sum_i r_i~~ < ~~5H\~~,</~~math>~~

	and

	:<~~math~~>~~u(z) \ge \frac{n}{2\pi}\log \frac{H}{e}~~<~~/math~~>

	for ~~all ''z~~'~~' outside~~ the ~~union~~ of ~~these discs~~.

	~~==Notes==~~

	~~<references/>~~

	~~{{mathanalysis-stub}}~~
	~~[[Category:Complex analysis]]~~

en>Duoduoduo: /* Formal definition */ dab link

2013-08-07T17:10:42Z

Formal definition: dab link

← Older revision		Revision as of 19:10, 7 August 2013
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	~~Im Dotty~~ and ~~was born~~ on ~~21 November 1981~~. ~~My hobbies are Photography and American football~~.<br><br>~~Feel free to visit my web blog~~: ~~[http~~://~~www.heavenlywallpapers.com~~/~~profile~~/~~widavila Size guaide mountain bike sizing~~.]		{{distinguish\|Cartan's theorem}}
			In [[potential theory]], a branch of [[mathematics]], '''Cartan's lemma''', named after [[Henri Cartan]], is a bound on the measure and complexity of the set on which a logarithmic [[Newtonian potential]] is small. The following statement can be found in Levin's book.<ref>B.Ya. Levin, ''Lectures on Entire Functions''</ref>

			Let ''μ'' be a finite positive [[Borel measure]] on the complex plane '''C''' with ''μ''('''C''') = ''n''. Let ''u''(''z'') be the logarithmic potential of ''μ'':

			:<math>u(z) = \frac{1}{2\pi}\int_\mathbf{C} \log\|z-\zeta\|\,d\mu(\zeta)</math>

			Given ''H'' ∈ (0, 1), there exist discs of radius ''r''<sub>''i''</sub> such that

			:<math>\sum_i r_i < 5H\,</math>

			and

			:<math>u(z) \ge \frac{n}{2\pi}\log \frac{H}{e}</math>

			for all ''z'' outside the union of these discs.

			==Notes==

			<references/>

			{{mathanalysis-stub}}
			[[Category:Complex analysis]]

111.69.243.91: /* Formal definition */ grammar

2010-07-23T15:45:31Z

Formal definition: grammar

New page

Im Dotty and was born on 21 November 1981. My hobbies are Photography and American football.<br><br>Feel free to visit my web blog: [http://www.heavenlywallpapers.com/profile/widavila Size guaide mountain bike sizing.]

Linear bottleneck assignment problem - Revision history

en>BD2412: minor fixes, mostly disambig links using AWB

en>Duoduoduo: /* Formal definition */ dab link

111.69.243.91: /* Formal definition */ grammar