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- {{Short description|Problem book in mathematical analysis}} ...cal analysis|analysis]] by [[George Pólya]] and [[Gábor Szegő]]. Published in 1925, the two volumes are titled (I) ''Series. Integral Calculus. Theory of ...10 KB (1,506 words) - 02:54, 22 February 2025
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- ...on differentiation''', named after [[Guido Fubini]], is a result in [[real analysis]] concerning the [[Derivative|differentiation]] of series of [[monotonic fu ...l <math>x \in I,</math> then for [[almost everywhere|almost any]] <math>x \in I,</math> the derivatives exist and are related as:<ref name="a"/> ...1 KB (214 words) - 20:14, 22 December 2022
- ...|mr=2009|pages=556–583|series=Second Series|title=On regularly convex sets in the space conjugate to a Banach space|volume=41|year=1940|issue=3 |jstor=19 Both of the following theorems are referred to as the Krein-Smulian Theorem. ...3 KB (361 words) - 16:47, 22 July 2024
- ...st=Axel Johannes |last=Malmquist|year1=1913|year2=1920|year3=1941}}. These theorems restrict the forms of first order algebraic [[differential equation]]s whic ==Statement of the theorems== ...3 KB (395 words) - 03:03, 10 May 2024
- {{Short description|Theorem in complex analysis about the sheaf of holomorphic functions}} ...h>) is [[coherent sheaf|coherent]].<ref>{{harvtxt|Noguchi|2019}}</ref><ref>In {{harvtxt|Oka|1950}} paper it was called the [[idéal de domaines indétermin ...2 KB (297 words) - 21:44, 26 October 2024
- In the theory of [[orthogonal functions]], '''Lauricella's theorem''' provides ..._k\}</math> [[Convergence_of_random_variables#Convergence_in_mean|converge in the mean]] to that function. ...853 bytes (118 words) - 10:07, 30 November 2024
- In mathematics, specifically in the study of [[vector bundle]]s over [[Kähler manifold|complex Kähler manif ...first2=Shigeo|date=1954|title=Note on Kodaira-Spencer's proof of Lefschetz theorems|url=https://projecteuclid.org/euclid.pja/1195526105|journal=Proceedings of ...3 KB (419 words) - 08:41, 5 March 2023
- In [[mathematics]], more specifically in [[functional analysis]], a subset <math>T</math> of a [[topological vector space]] <math>X</math> This condition arises frequently in many theorems of functional analysis. ...1 KB (142 words) - 19:51, 12 August 2023
- ...] and [[Norman George Meyers]], states that [[smooth functions]] are dense in the [[Sobolev space]] <math>W^{k,p}(\Omega)</math> ...n ended much confusion about the relationship of these spaces that existed in the literature before that time. It is surprising that this elementary resu ...2 KB (298 words) - 12:19, 12 December 2024
- {{Short description|Mathematical theorem in convex analysis}} ...lization of the [[bipolar theorem]].<ref name="BorweinLewis"/> It is used in [[duality (optimization)|duality theory]] to prove [[strong duality]] (via ...3 KB (372 words) - 19:53, 5 April 2023
- In [[mathematics]], '''Dieudonné's theorem''', named after [[Jean Dieudonné]], ...escu">{{cite book |last=Zălinescu |first=Constantin |title=Convex analysis in general vector spaces |publisher=World Scientific Publishing Co.,  ...1 KB (173 words) - 01:52, 23 October 2022
- In mathematics, the '''Grace–Walsh–Szegő coincidence theorem'''<ref>{{cite jou * multi-affine, i.e. [[Affine transformation|affine]] in each variable separately. ...2 KB (228 words) - 04:30, 16 December 2024
- ...ntrol]], and [[mathematical economics]].<ref>{{cite book|title=Fixed Point Theorems with Applications to Economics and Game Theory|last=Border|first=Kim C.|pub : <math>\forall x \in X: \,\,\, f(x) \in F(x) \,.</math> ...7 KB (989 words) - 23:38, 30 May 2024
- ...everywhere of operator averages |journal=Journal of Rational Mechanics and Analysis |volume=5 |year=1956 |pages=129–178 |mr=77090 }}.</ref> exists almost everywhere for all <math display="inline">f\in L^1</math>. ...1 KB (203 words) - 02:11, 9 February 2025
- ....<ref>{{cite book|last1=Aliprantis|last2=Border|title=Infinite-dimensional analysis. A hitchhiker's guide.|date=2006}}</ref><ref>{{cite book|first=Alexander S. ...st3=José |date=2010 |title=Measurability and Selections of Multi-Functions in Banach Spaces ...3 KB (418 words) - 17:38, 21 June 2023
- ...heorem was originally formulated by [[Giulio Vivanti ]] in 1893 and proved in the following year by [[Alfred Pringsheim]]. *I-hsiung Lin: ''Classical Complex Analysis: A Geometric Approach (Volume 2)''. World Scientific Publishing Company, 20 ...1 KB (214 words) - 23:15, 13 February 2025
- ...rem''' is a result in the field of [[functional analysis]]. It states that in a [[unital algebra|unital]] [[C*-algebra]], the closure of the [[convex hul ...A. Belfi | title = Characterizations of C*-Algebras: The Gelfand–Naimark Theorems | publisher = Marcel Dekker | location = New York | year = 1986 | isbn = 0- ...2 KB (375 words) - 01:37, 5 November 2020
- ...istinct from) the [[Weak topology|weak convergence]] in [[Banach space]]s. In [[Hilbert space]], Delta-convergence and weak convergence coincide. For a g ...d by Teck-Cheong Lim,<ref name="Lim">T.C. Lim, Remarks on some fixed point theorems, Proc. Amer. Math. Soc. '''60''' (1976), 179–182.</ref> and, soon after, un ...4 KB (547 words) - 20:21, 13 September 2021
- In mathematics, '''Arakelyan's theorem''' is a generalization of [[Mergelyan's ...e interior of ''E'' and for every ''ε'' > 0 there exists ''g'' holomorphic in Ω such that |''g'' − ''f''| < ''ε'' on ''E'' if and onl ...2 KB (239 words) - 00:21, 22 January 2025
- ...t if <math>K</math> is a nonempty [[convex set|convex]] closed bounded set in uniformly convex [[Banach space]] and <math>f</math> is a mapping of <math> ...otic center is [[Delta-convergence|Delta-limit]] of Teck-Cheong Lim, which in the uniformly convex space coincides with the weak limit if the space has t ...2 KB (295 words) - 21:32, 23 August 2024
- ...the conditions stated below, [[integrable]] functions can be approximated in L<sup>1</sup> from above and below by lower- and [[upper-semicontinuous]] f | title = Real and Complex Analysis ...1 KB (185 words) - 20:06, 18 May 2024