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Equicontinuity - Wikipedia, the free encyclopedia As promised in the introduction, the limit of a pointwise convergent, equicontinuous sequence is continuous. Furthermore, equicontinuity and pointwise convergence imply uniform convergence. The most general scenario in which equicontinuity can be defined is for topological spaces whereas uniform equicontinuity requires the filter of neighbourhoods of one point to be somehow comparable with the filter of neighbourhood of another point. en.wikipedia.org /wiki/Equicontinuity   (640 words)

Equicontinuity -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: 2007-11-07) The definition for equicontinuity generalizes to functions between arbitrary (A set of points such that for every pair of points there is a nonnegative real number called their distance that is symmetric and satisfies the triangle inequality) metric spaces. The most general scenario in which equicontinuity can be defined is for ((mathematics) any set of points that satisfy a set of postulates of some kind) topological spaces whereas uniform equicontinuity requires the filter of neighbourhoods of one point to be somehow comparable with the filter of neighbourhood of another point. A set of functions A between two topological spaces X and Y is equicontinuous at the point x ∈ X if for every neighbourhood V of f(x), there is some neighbourhood U of x such that for every function f in A, f(U) ⊆ V. www.absoluteastronomy.com /encyclopedia/E/Eq/Equicontinuity.htm   (818 words)

Equicontinuity   (Site not responding. Last check: 2007-11-07) } be an equicontinuous sequence of functions from X ⊂ R to R. } be an equicontinuous sequence of functions from [0, 1] to R. } be an equicontinuous sequence of uniformly bounded functions from [0, 1] to R. www.sciencedaily.com /encyclopedia/equicontinuity   (756 words)

Equicontinuity   (Site not responding. Last check: 2007-11-07) En análisis matemático, una secuencia de funciones es equicontinuous si todas las funciones son contínuas y tienen excedente igual de la variación una vecindad dada (una definición exacta aparece abajo). Teorema 3: Cada secuencia de funciones equicontinuous a partir de la 0, 1 a R es uniformemente equicontinuous. El panorama más general en el cual el equicontinuity puede ser definido está para los espacios topológicos mientras que el equicontinuity uniforme requiere el filtro de vecindades de un punto ser de alguna manera comparable con el filtro de la vecindad de otro punto. www.yotor.net /wiki/es/eq/Equicontinuity.htm   (761 words)

No Title   (Site not responding. Last check: 2007-11-07) defined on E is said to be equicontinuous if for all (a) Assume that an equicontinuous sequence of functions converges uniformly on a compact set E, then the sequence is equicontinuous. www.math.psu.edu /kra/mat404/hw9/hw9.html   (126 words)

PlanetMath: Ascoli-Arzelà theorem   (Site not responding. Last check: 2007-11-07) is equibounded and uniformly equicontinuous then there exists a uniformly convergent subsequence Recall, in fact, that a subset of a complete metric space is totally bounded if and only if its closure is compact (or sequentially compact). Cross-references: convergent, image, sequentially compact, compact, closure, metric space, complete, induced, metric, uniform convergence, mappings, continuous, totally bounded, subsequence, uniformly convergent, uniformly equicontinuous, equibounded, functions, sequence, subset, bounded planetmath.org /encyclopedia/AscoliArzelaTheorem.html   (142 words)

Equicontinuity of families of plurisubharmonic functions with bounds on their Monge-Ampère masses. - Ko ...   (Site not responding. Last check: 2007-11-07) Equicontinuity of families of plurisubharmonic functions with bounds on their Monge-Ampère masses. Equicontinuity of families of plurisubharmonic functions with bounds on their Monge-Ampère masses (2001) Ko/lodziej, Equicontinuity of families of plurisubharmonic functions with bounds on their Monge-Amp`ere masses, preprint. citeseer.ist.psu.edu /kolodziej01equicontinuity.html   (437 words)

Abstract of my thesis   (Site not responding. Last check: 2007-11-07) The first part is a study of equicontinuous pseudogroups. If (M,F) is a equicontinuous foliation on a compact manifold then we show that the closure of leaves makes a partition and the foliation has a transversal "good measure". We prove that equicontinuous conformal foliations are Riemannian. www.umpa.ens-lyon.fr /~ctarquin/abstract.html   (218 words)

LaTeX bugs database The topology on $\pin E$ is the topology of uniform convergence on the equicontinuous subsets of the dual $\big(\pin E \big)'=\sP(^nE)$, while the topology on $(\sP(^nE),\t_0)_\b'$ is the topology of uniform convergence on the $\t_0$-bounded, or, by (\cite{din}, Lemma 1.23), the $\t_b$-bounded subsets of $\sP(^nE)$. Since $(\sP(^nE),\t_\omega)$ is barrelled, the equicontinuous subsets of its dual coincide with the $\t$-bounded subsets of $\sP_{HY}(^nE_\b')$. Since $(x_i)_i$ is a countable bounded subset of $E_{\b \b}''$, it is equicontinuous and hence there exists a bounded subset $B$ in $E$ such that $(x_i)_i\subset \bpol{B}$. www.latex-project.org /cgi-bin/ltxbugs2html?pr=latex/3560   (7944 words)

Abstract   (Site not responding. Last check: 2007-11-07) It turns out that a system is weakly mixing if and only if any pair not in the diagonal is a sequence entropy pair if and only if the same holds for a weak mixing pair, answering an open question by Blanchard, Host and Maass. For a group action we show that the factor induced by the smallest invariant equivalence relation containing weak mixing pairs is equicontinuous, supplying another proof concerning regionally proximal relation. Furthermore, for a minimal distal system the set of sequence entropy pairs coincides with the regionally proximal relation and thus a non-equicontinuous minimal distal system is not null. www.math.iit.edu /events/ye_abs.html   (273 words)

AMCA: Equicontinuous families and applications to von Neumann algebras and stochastic integration in Banach spaces by ...   (Site not responding. Last check: 2007-11-07) This talk is devoted to a study of equicontinuous families of measures and how they apply to the Brooks-Chacon Biting Lemma. We shall discuss applications (done jointly with K. Saito and J.D.M. Wright) to von Neumann algebras: A Dieudonne'-type theorem and a "nearly weakly convergent" subsequence theorem for normal functionals is presented. The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. at.yorku.ca /c/a/k/c/41.htm   (132 words)

[No title] Yes if the functions are equicontinuous, but not in general. However, if the functions are uniformly equicontinuous and the domain is compact, then pointwise convergence implies uniform convergence. This is not enough, for instance consider a discrete space with atoms of arbitrarily small measure. www.math.ucla.edu /~tao/java/MultipleChoice/convergence.txt   (2198 words)

Atlas: On equicontinuous and almost equicontinuous cellular automata by Emily Gamber   (Site not responding. Last check: 2007-11-07) Naturally, one is interested in determining when such a system is either equicontinuous or sensitive (sdic). In one dimension, almost equicontinuous cellular automata can be characterized by the existence of 'blocking' words. Equicontinuous cellular automata are ones for which every long enough word is blocking. atlas-conferences.com /cgi-bin/abstract/capc-45   (140 words)

[No title] 14386 Robert Ellis/Harvey Keynes: A characterization of the equicontinuous structure relation. Gray/Roberson: On the near equicontinuity of transformation groups. Willima Veech: The equicontinuous structure relation for minimal abelian transformation groups. felix.unife.it /Root/d-Mathematics/d-Dynamical-systems/d-Topological-dynamics/b-Topological-dynamics   (874 words)

Auslander Abstract   (Site not responding. Last check: 2007-11-07) Certain classes, in particular those which are equicontinuous and distal, have been intensively studied, and we will discuss the structure of these flows. A "Galois theory", based on subgroups of the automorphism group of the universal minimal flow, provides a partial classification of minimal flows. To this end, we make use of the capturing operation, a kind of reverse orbit closure, which was introduced by Glasner and myself to characterize the distal and equicontinuous structure relations. www.math.uiuc.edu /Colloquia/03SP/auslander_may1-03.html   (131 words)

Math 444 Homework Assignments Unless specified otherwise, all problems are from the class text. Let (f_n) be a sequence of functions that are pointwise bounded (i.e. Suppose {f_n} is equicontinuous on  [a,b] and f_n -> f pointwise. www.math.uiuc.edu /~pjanakir/385/homework.html   (601 words)

Reverse mathematics - Wikipedia, the free encyclopedia The sequential completeness of the real numbers (every bounded increasing sequence of real numbers has a limit). Ascoli's theorem: every bounded equicontinuous sequence of real functions on the unit interval has a uniformly convergent subsequence. Every countable commutative ring has a maximal ideal. en.wikipedia.org /wiki/Reverse_mathematics   (3382 words)

Abstract - Francesco Altomare   (Site not responding. Last check: 2007-11-07) Francesco Altomare : Convergence Problems for Equicontinuous Sequences of Linear Operators on Banach Spaces The most classical development of Korovkin-type approximation Theory essentially dealt with simple criteria ensuring the convergence of arbitrary sequences of positive linear operators toward the identity operator. There is also a plain copy of this text. adela.karlin.mff.cuni.cz /katedry/kma/ss/apr97/altomare.htm   (213 words)

No Title The key idea of equicontinuity is that inequality (14) holds simultaneously for all There is a classical theorem of functional analysis, Ascoli's Theorem that relates uniform equicontinuity to uniform convergence: be a sequence of strongly uniformly stochastically equicontinuous functions from gemini.econ.umd.edu /jrust/econ551/lectures/ucproof/ucproof.html   (748 words)

[No title]   (Site not responding. Last check: 2007-11-07) Let $E$ be a sequentially complete locally convex topological vector space, and let $A$ be a linear operator in $E$. Then the following two statements are equivalent: \item{i)} $A$ is the infinitesimal generator of a strongly continuous equicontinuous semigroup of transformations in $E$. \item{ii)} The domain of $A$ is dense in $E$ and $$ \left\{\left(I-n^{-1}A\right)^{-m}: m,n=1,2,\ldots\right\} $$ is an equicontinuous collection of linear operators on $E$. www.maths.tcd.ie /EMIS/journals/EJDE/Monographs/Volumes/1993/01-Dorroh-Neuberger/Dorroh-tex   (2699 words)

[No title]   (Site not responding. Last check: 2007-11-07) There exists a function with a jump discontinuity at exactly every rational number. The limit of a convergent sequence of equicontinuous functions is equicontinuous. If a sequence of differentiable functions converges uniformly to a limit, then the derivatives also converge. www.people.fas.harvard.edu /~bgchen/55afinrev.html   (279 words)

F. Equicontinuity Thm A function f(x) is said to be equicontinuous on an interval [a,b] if and only if for each The proof given below holds in the case of a function of one variable. It can be generalized to provide the demonstration of a theorem on the equicontinuity of functions of several variables. www.whyslopes.com /etc/Real-Analysis-Decimal-View/appF4-Equicontinuity.html   (667 words)

TVP Volume 9 Issue 2 By using LOCUS you agree to abide by the In the paper we study limit properties of equicontinuous (nearly periodic) positive operators which transform continuous functions into continuous ones. The domain of definition of the functions is a compact Hausdorff space $X$. locus.siam.org /TVP/volume-09/art_1109033.html   (199 words)

[No title] If {X} is a compact Hausdorff space and F is an equicontinuous, pointwise bounded subset of the space C(X) of continuous functions on X, then F is totally bounded in the uniform metric and the closure of F in C(X) is compact. } is an equicontinuous, pointwise bounded sequence in C(X), then there exists a subsequence and an f in C(X) such that the subsequence converges to f uniformly on compact sets. A subset S of C[0,1] is called equicontinuous at x in [a,b] if for any www.mathacademy.com /platonic_realms/encyclop/main.txt   (8404 words)

Abstracts   (Site not responding. Last check: 2007-11-07) November, 2001 and in revised form on 14 May, 2002 AMS classification 47 D 03, 47 A 58, 35 K 65. In this paper we prove Trotter-Kato approximation results and the Lie-Trotter product formula for locally equicontinuous semigroups on sequentially complete locally convex spaces. www.math.unipr.it /~rivista/dati/2002+*/Albanese.html   (87 words)

[No title]   (Site not responding. Last check: 2007-11-07) it is bounded and equicontinuous" > > My problem is going from bounded and equicontinuous -> compact. In > particular he uses a diagonalization which I can't seem to grasp. Now he finishes by showing that equicontinuity can be used to prove the sequence of functions is uniformly convergent. www.math.niu.edu /~rusin/known-math/01_incoming/ascoli   (275 words)

On the Purification of Nash Equilibria of Large Games We consider Salim Rashid's asymptotic version of David Schmeidler's theorem on the purification of Nash equilibria. We show that, in contrast to what is stated, players' payoff functions have to be selected from an equicontinuous family in order for Rashid's theorem to hold. That is, a bound on the diversity of payoffs is needed in order for such asymptotic result to be valid. ideas.repec.org /p/wpa/wuwpga/0311007.html   (270 words)

Math 213a: Complex Analysis (Fall 2003) (C) of a normal family of analytic functions from Omega to a Riemann surface S. In general, a family of continuous functions on a metric space with a countable covering by compact subspaces is normal iff it is uniformly bounded and equicontinuous on compacta. When we're dealing with analytic functions, equicontinuity is implied by uniform boundedness of the derivative. The hard part is showing that the limit of a sequence of functions u whose I(u) approach the infimum is again continuously differentiable, and then to show that it is in fact harmonic. www.math.harvard.edu /%7Eelkies/M213a.03/index.html   (2377 words)

Portugaliæ Mathematica, Vol. 57, No. 3, pp. 329-344, 2000   (Site not responding. Last check: 2007-11-07) {\bf 3}) $C_{\varphi}$ maps some 0-neighbourhood into an equicontinuous, a compact or a weakly compact set; {\bf 4}) $C_{\varphi}$ maps any bounded set into an equicontinuous, a compact or a weakly compact set. This page was last modified: 31 Jan 2003. www.math.ethz.ch /EMIS/journals/PM/57f3/7.html   (196 words)

On the Existence of Pure Strategy Nash Equilibria in Large Games We consider an asymptotic version of Mas-Colell's theorem on the existence of pure strategy Nash equilibria in large games. Our result states that, if players' payoff functions are selected from an equicontinuous family, then all sufficiently large games have an epsilon - pure, epsilon - equilibrium for all epsilon greater than 0. We also show that our result is equivalent to Mas-Colell's existence theorem, implying that it can properly be considered as its asymptotic version. ideas.repec.org /p/wpa/wuwpga/0412008.html   (294 words)

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