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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"/> ...

...the conditions stated below, [[integrable]] functions can be approximated in L¹ from above and below by lower- and [[upper-semicontinuous]] f | title = Real and Complex Analysis ...

...the Fourier series of a periodic function ''f'' converges uniformly on the real line if [[Category:Theorems in Fourier analysis]] ...

{{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 ...

...heorem was originally formulated by [[Giulio Vivanti ]] in 1893 and proved in the following year by [[Alfred Pringsheim]]. with non-negative real coefficients <math>a_n</math> and a [[radius of convergence]] <math>R</math ...

...ós' theorem''' is a theorem from [[probability theory]] and [[mathematical analysis]] about the [[Cesàro summation|Cesàro convergence]] of a [[subsequence]] of The theorem was proven in 1967 by [[János Komlós (mathematician)|János Komlós]].<ref>{{cite journal|a ...

[[File:elastic load method (full).png|thumb|right|300px|(0) real beam, (1) shear and moment, (2) conjugate beam, (3) slope and displacement] ...ler 2009 328–335">{{cite book |last=Hibbeler |first=R.C. |title=Structural Analysis |url=https://archive.org/details/structuralanalys00hibb_770|url-access=limi ...

...ph L. Walsh]] in 1929, using results proved by [[Henri Lebesgue|Lebesgue]] in 1907.<ref>{{cite journal|author=Walsh, J. L.|title=Über die Entwicklung ein ...<math>\partial{K}</math> by (real-valued) [[harmonic polynomial]]s in the real variables {{math|x}} and {{math|y}}.<ref>{{cite book|author=Gamelin, Theodo ...

In [[mathematical analysis]], '''Krein's condition''' provides a necessary and sufficient condition fo \quad a_k \in \mathbb{C}, \, \lambda_k \geq 0 \right\},</math> ...

In [[mathematics|mathematical]] [[abstract harmonic analysis|harmonic analysis]], '''Harish-Chandra's ''Ξ'' function''' is a [[special function|special]] *''a''(''g'') is the element ''a'' in the Iwasawa decomposition ''g''=''nak'' ...

In [[mathematics]], '''Fuchs' theorem''', named after [[Lazarus Fuchs]], state for some positive real ''s'', or ...

[[File:Chord graph.png|thumb| A chord (in red) of length 0.3 on a sinusoidal function. The universal chord ...n for every [[natural number]] <math>n</math>, there exists some <math> x \in [a,b] </math> such that <math> f(x) = f\left(x + \frac{b-a}{n}\right) </mat ...

...refers to two closely related theorems in [[general topology]] and [[real analysis]], named after [[Georg Cantor]], about intersections of decreasing nested [ ...ty compact, closed subsets of <math>S</math> has a non-empty intersection. In other words, supposing <math>(C_k)_{k \geq 0}</math> is a sequence of non-e ...

...e [[complex number]]s <math>\mathbb{C}</math>) to linear operators valued in [[topological vector space]]s (TVSs). In order for a TVS {{mvar|Y}} to have the extension property, it must be [[Com ...

The '''Bohr–Favard inequality''' is an inequality appearing in a problem of [[Harald Bohr]]<ref name="bohr1935theoreme">{{Cite journal |au </ref> on the boundedness over the entire real axis of the integral of an almost-periodic function. The ultimate form of t ...

{{short description|Uniqueness for linear partial differential equations with real analytic coefficients}} ...s a uniqueness result for linear [[partial differential equations]] with [[real analytic]] coefficients.<ref>Eric Holmgren, "Über Systeme von linearen part ...

...0019811.15510.27|bibcode=2004JSP...115..185L|arxiv=math-ph/0210027}}</ref> In 2015, [[Alexandre Eremenko]] gave a simplified proof of Stahl's theorem.<re In 2023, [[Otte Heinävaara]] proved a structure theorem for [[Hermitian matric ...

...pondence]] between [[jordan algebra#Formally real Jordan algebras|formally real Jordan algebras]] and so-called domains of positivity. Thus it links [[oper ...' if <math>a=0</math> whenever both <math>a</math> and <math>-a</math> are in the closure <math>\overline{C}</math>. ...

In the [[mathematics|mathematical]] field of [[complex analysis]], '''Akhiezer's theorem''' is a result about [[entire function]]s proved b ...f [[exponential type]] <math>\tau</math>, with <math>f(x)\geq 0</math> for real <math>x</math>. Then the following are equivalent: ...

{{Short description|Proposition in complex analysis introduced by William Fogg Osgood}} ...several [[complex variable]]s that is [[holomorphic function|holomorphic]] in each variable separately is holomorphic. The assumption that the function i ...