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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.)

1905
*
Mathematical Gazette
*

Sans ce principe d’indépendance,

doi:10.1017/s0025557200239478
fatcat:dfkubufczre2jczsgoefvazfkq
*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 ...##
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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*. ...

##
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Lecons sur les fonctions de variables reelles

1905
*
Mathematical Gazette
*

These are

doi:10.2307/3602360
fatcat:ror5kmlnabfydifqe26kfhseve
*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. ...##
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Zornian Functional Analysis or: How I Learned to Stop Worrying and Love the Axiom of Choice
[article]

2020
*
arXiv
*
pre-print

As this is a text aimed for analysis students, we will not focus

arXiv:2010.15632v1
fatcat:4u5njn2xhre6nnauh3w6fcbjum
*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 ...##
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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. ...##
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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. ...##
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Semi-Groups of Analytic Maps

2001
*
Computational methods in Function Theory
*

We consider a generalization, due to Baker and Rippon, of a version of the Denjoy-Wolff

doi:10.1007/bf03320988
fatcat:khnpa3dcwvhozmfjfav3r2gntq
*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. ...##
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On geometric automata which can nondeterministically choose auxiliary points

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. ...

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

2015
*
arXiv
*
pre-print

In

arXiv:1502.01548v2
fatcat:i2c5ngvo2fh4ln6undsmewqcva
*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. ...##
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Oscillating singularities in Besov spaces

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

doi:10.1016/j.matpur.2004.01.001
fatcat:owiphexlvjdvpotj2vo7neqqqm
*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. ...##
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Dynamics in one complex variable: introductory lectures
[article]

1990
*
arXiv
*
pre-print

These lectures are intended to introduce the reader to

arXiv:math/9201272v1
fatcat:52kd3aop7far5gnwaymk7w6aqq
*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. ...##
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Directional Thermodynamic Formalism

2019
*
Symmetry
*

Secondly, we performed the directional multifractal formalism, i.e., we computed or estimated directional Hölder spectra, either directly or via

doi:10.3390/sym11060825
fatcat:mhufkkhxg5fbvdivd4sns2mrwi
*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. ...##
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Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of CP(k)

2018
*
Annales Scientifiques de l'Ecole Normale Supérieure
*

This is coherent with the

doi:10.24033/asens.2355
fatcat:v74oj5cvdjfobohgznx47kdomy
*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 . ...##
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Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of CP(k)
[article]

2016
*
arXiv
*
pre-print

Our methods deeply exploit the properties of Lyapunov exponents and are based

arXiv:1403.7603v3
fatcat:r5ovfs5oazbkxngogurevxkgoq
*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. ...##
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On the vanishing of reduced 1-cohomology for Banach representations

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. ...

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