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Leçons sur les fonctions de variables réelles, par E. Borel; Leçons sur les fonctions discontinues, par René Baire; Le calcul des residus et ses applications à la théorie des fonctions, par E. Lindelöf. (Paris, Gauthier-Villars, 1905, 3 f. 50 c. each.)

G. H. Hardy
1905 Mathematical Gazette  
Sans ce principe d’indépendance, on aurait eu tous les inconvénients d’un grand Traité, sans en avoir les avantages.’ In principle, no doubt M. Borel is right.  ...  A short but clear account follows of some familiar applications of the formula ale LO a and of some others which are not so familiar, such as occur in the proof of Jensen’s theorem, the theory of the Bernoullian  ... 
doi:10.1017/s0025557200239478 fatcat:dfkubufczre2jczsgoefvazfkq

Page 4862 of Mathematical Reviews Vol. , Issue 85k [page]

1985 Mathematical Reviews  
Grande, Zbigniew Deux remarques sur les dérivées partielles. [Two remarks on partial derivatives] Demonstratio Math. 16 (1983), no. 4, 961-964.  ...  For proving Theorem I we need topological tools, especially the theory of the (local) degree of a mapping, and Baire’s category theorem.  ... 

Lecons sur les fonctions de variables reelles

G. H. Hardy, E. Borel, Rene Baire, E. Lindelof
1905 Mathematical Gazette  
These are on Projective Geometry and Hyperspace.  ...  This high standard has not been maintained in all of the later volumes, some of which have been rather scrappy, and have given the impression of hasty, and at times perfunctory composition.  ...  Sans ce principe d'independance, on aurait eu tous les inconvenients d'un grand Traite, sans en avoir les avantages.' In principle, no doubt M. Borel is right.  ... 
doi:10.2307/3602360 fatcat:ror5kmlnabfydifqe26kfhseve

Zornian Functional Analysis or: How I Learned to Stop Worrying and Love the Axiom of Choice [article]

Asaf Karagila
2020 arXiv   pre-print
As this is a text aimed for analysis students, we will not focus on the set theoretic proofs or dwell on any particular set theoretic assumptions that are needed in order to prove certain results.  ...  This text is meant for analysis students who want to learn more about the effects of the axiom of choice on functional analysis, and the things that may go wrong in its absence.  ...  Ben-Artzi to submit this work as a final project; Theo Bühler whose encyclopedic knowledge regarding historical results and various references is uncanny, and helped in clearing out some issues; Matt Foreman  ... 
arXiv:2010.15632v1 fatcat:4u5njn2xhre6nnauh3w6fcbjum

Page 6391 of Mathematical Reviews Vol. , Issue 91M [page]

1991 Mathematical Reviews  
Call a one-to-one mapping V:R — NN a representation of R, where R is the set of real numbers and NN is the set of number-theoretic functions (Baire’s zero-space).  ...  Finally the Spector-Gandy theorem is discussed in the present setting and some limitations are shown.  ... 

Page 1918 of Mathematical Reviews Vol. , Issue 95d [page]

1995 Mathematical Reviews  
The author suggests that these remarks may have been the reason why Fatou did not enter the prize contest. Consequently, Julia was awarded the Grand Prix, a natural deci- sion as other entries by S.  ...  Baire’s 1905 paper [Acta Math. 30 (1905), 1-48; Jbuch 36, 453]; (7) the mate- rials to the course on set theory taught by Luzin in 1916.  ... 

Semi-Groups of Analytic Maps

Alan F. Beardon
2001 Computational methods in Function Theory  
We consider a generalization, due to Baker and Rippon, of a version of the Denjoy-Wolff Theorem that is applicable to repeated compositions of different analytic self-maps of the unit disc D.  ...  Then D is the countable union of the D m , and so by Baire's Category Theorem, some D m is dense in some open subset of D.  ...  In particular, we need to eliminate the use (in [2] ) of the Denjoy-Wolff Theorem. Section 4 contains some closing remarks and extensions of these results.  ... 
doi:10.1007/bf03320988 fatcat:khnpa3dcwvhozmfjfav3r2gntq

On geometric automata which can nondeterministically choose auxiliary points

Ulrich Huckenbeck
1990 RAIRO - Theoretical Informatics and Applications  
On the other hand we shall prove some gênerai results about the different power of -GCM 0 's and ^'-GCM 0 's; these results are obtained by topological and fixed point theoretical means. Résumé.  ...  Avant tout, nous voulons comparer les capacités de ces machines: Pour une grande classe de paires (3F, &') nous démontrons que les modèles 3F-GCM 0 et tF'-GCM 0 sont équivalents.  ...  But then Baire's category theorem says that the open kernel of the countable union ï/ p) must also be empty.  ... 
doi:10.1051/ita/1990240504711 fatcat:nwt565gyjfbfpntpkefy2is5oy

A Scalar Associated with the Inverse of Some Abelian Integrals and a Ramified Riemann Domain [article]

Junjiro Noguchi
2015 arXiv   pre-print
In one dimensional case, we apply the obtained estimate of ρ(a, Ω) to give a new proof of Behnke-Stein's Theorem for the Steiness of open Riemann surfaces.  ...  We obtain some geometric conditions in terms of ρ(a, X) which imply the validity of the Levi problem for a finitely sheeted Riemann domain over ^n.  ...  The author is very grateful to Professor Makoto Abe for interesting discussions on the present theme.  ... 
arXiv:1502.01548v2 fatcat:i2c5ngvo2fh4ln6undsmewqcva

Oscillating singularities in Besov spaces

C. Melot
2004 Journal des Mathématiques Pures et Appliquées  
That is why Uriel Frisch and Giorgio Parisi proposed an algorithm which relates these dimensions d(h) to some averaged increments.  ...  These results show that in many function spaces, quasi-all functions (in the sense of Baire's categories) do not obey the multifractal formalism if the Hölder exponent is large.  ...  Acknowledgements The author is very grateful to Yanick Heurteaux, Stéphane Jaffard, and Yves Meyer for many comments on this text.  ... 
doi:10.1016/j.matpur.2004.01.001 fatcat:owiphexlvjdvpotj2vo7neqqqm

Dynamics in one complex variable: introductory lectures [article]

John W. Milnor
1990 arXiv   pre-print
These lectures are intended to introduce the reader to some key ideas in the field, and to form a basis for further study.  ...  They are based on introductory lectures given at Stony Brook during the Fall Term of 1989-90.  ...  By Baire's Theorem, any such countable intersection is itself a dense subset of J . Corollary.  ... 
arXiv:math/9201272v1 fatcat:52kd3aop7far5gnwaymk7w6aqq

Directional Thermodynamic Formalism

Mourad Ben Ben Slimane, Moez Ben Ben Abid, Ines Ben Omrane, Borhen Halouani
2019 Symmetry  
Secondly, we performed the directional multifractal formalism, i.e., we computed or estimated directional Hölder spectra, either directly or via some Legendre transforms on either directional scaling function  ...  It is based on a scaling function characterized in terms of isotropic Sobolev or Besov-type norms. The purpose of the present paper was twofold.  ...  Remark 10. The new formalism shows also that if D(H, e) in Theorem 6 is replaced by D T (H, e) then we get optimality independently on the choice of A. Theorem 10.  ... 
doi:10.3390/sym11060825 fatcat:mhufkkhxg5fbvdivd4sns2mrwi

Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of CP(k)

François Berteloot, Fabrizio Bianchi, Christophe Dupont
2018 Annales Scientifiques de l'Ecole Normale Supérieure  
This is coherent with the one-dimensional definition of the bifurcation current, due to DeMarco [dM]. We stress that Theorem 1.1 stays partially true for general families (see Theorem 1.6).  ...  An equilibrium lamination is a relatively compact subset (3) Γ γ does not meet the grand orbit of the critical set of f for every γ ∈ L, (4) the map F : L → L is d k to 1.  ...  The proof of Theorem 1.8 relies on a Baire's category argument based on the continuity properties of λ → C + λ and λ → (C + ) λ .  ... 
doi:10.24033/asens.2355 fatcat:v74oj5cvdjfobohgznx47kdomy

Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of CP(k) [article]

François Berteloot, Christophe Dupont
2016 arXiv   pre-print
Our methods deeply exploit the properties of Lyapunov exponents and are based on ergodic theory and on pluripotential theory.  ...  notion of stability for equilibrium measures in holomorphic families of endomorphisms of CP(k) and prove that it is equivalent to the stability of repelling cycles and equivalent to the existence of some  ...  We will exploit here our results to get some informations on these loci. 6.1. Remarkable elements in bifurcation loci.  ... 
arXiv:1403.7603v3 fatcat:r5ovfs5oazbkxngogurevxkgoq

On the vanishing of reduced 1-cohomology for Banach representations

Yves Cornulier, Romain Tessera
2021 Annales de l'Institut Fourier  
On donne une nouvelle preuve géométrique du théorème de Delorme, s'étendant à une plus grande classe de groupes, dont les groupes algébriques résolubles p-adiques et les groupes résolubles de type fini  ...  On déduit, par exemple, un théorème ergodique pour les cocycles intégrables, ainsi qu'une nouvelle preuve du résultat de Bourgain disant qu'un arbre 3-régulier ne se plonge quasi-isométriquement dans aucun  ...  By Baire's theorem, there exists V n with ANNALES DE L'INSTITUT FOURIER non-empty interior.  ... 
doi:10.5802/aif.3363 fatcat:gdevtzbaivfjtbmuk3yv2g3ywi
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