Skip to main content
SpringerLink
Log in

Sur le théorème de recouvrement de Vitali

L’apprivoisement des constructions ensemblistes infinies

  • Published:
Archive for History of Exact Sciences Aims and scope Submit manuscript

Résumé

L’essentiel sur les recouvrements à la Vitali peut être exposé dans le cadre des familles d’intervalles de \({\mathbf{R}}\) et de leurs points d’accumulation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  • Aliprantis Charalambos D., Owen Burkinshaw (1990) Principles of real analysis (2nd ed). Academic Press, San Diego

    MATH  Google Scholar 

  • Austin Donald. (1965) A geometric proof of the Lebesgue differentiation theorem. Proceedings of the American Mathematical Society 16: 220–221

    Article  MathSciNet  MATH  Google Scholar 

  • Stefan Banach, (1924) Sur le théorème de M. Vitali. Fund. Math. 5: 130–136

    Google Scholar 

  • Besicovitch Abram S. (1945) A general form of the covering principle and relative differentiation of additive functions. Proceedings of the Cambridge Philosophical Society 41: 103–110

    Article  Google Scholar 

  • Borel Émile. (1898) Leçons sur la théorie des fonctions. Gauthier-Villars, Paris

    MATH  Google Scholar 

  • Botsko Michael W. (2003) An elementary proof of Lebesgue’s differentiation theorem. American Mathematical Monthly 110: 834–838

    Article  MathSciNet  MATH  Google Scholar 

  • Carathéodory Constantin. (1918) Vorlesungen über reelle Funktionen. Leipzig, Teubner

    MATH  Google Scholar 

  • Denjoy Arnaud. (1915) Mémoire sur les nombres dérivés des fonctions continues. J. Math. Pures et Appl. 7: 105–240

    Google Scholar 

  • Evans Lawrence C., Ronald F. Gariepy. (1992) Measure theory and fine properties of functions. CRC Press, Boca Raton

    MATH  Google Scholar 

  • Hawkins, Thomas H. 1970. Lebesgue’s theory of integration. Its origins and development. Chelsea publishing company.

  • Hildebrandt Theophil H. (1963) Introduction to the theory of integration. Academic Press, New York

    Google Scholar 

  • Leader Solomon. (2001) The Kurzweil-Henstock integral and its differentials. Marcel Dekker, New York

    MATH  Google Scholar 

  • Lebesgue Henri. (1904) Leçons sur l’intégration et la recherche des fonctions primitives. Gauthier-Villars, Paris

    Google Scholar 

  • Lebesgue Henri. (1905) Sur les fonctions représentables analytiquement. J. de Math. Pures et Appl. 6: 139–216

    Google Scholar 

  • Lebesgue Henri. (1910) Sur l’intégration des fonctions discontinues. Ann. École Normale Supérieure 27(3): 361–450

    MathSciNet  MATH  Google Scholar 

  • Lusin Nicolas N. (1917) Sur la classification de M. Baire. Comptes Rendus Acad. Sci. Paris 164: 91–94

    Google Scholar 

  • Lusin, Nicolas N. 1927. Sur les ensembles analytiques. Fundamenta Math. 10: 1–95.

    Google Scholar 

  • Melas Antonios D. (2003) The best constant for the centered Hardy–Littlewood maximal inequality. Annals of Mathematics 157: 647–688

    Article  MathSciNet  MATH  Google Scholar 

  • Michel Alain. (1992). Constitution de la Théorie moderne de l’Integration. Vrin 117

  • Natanson, Isidor P. 1955. Teoriya funkciĭ veščestvennoĭ peremennoĭ. Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscou-Leningrad, 1950. Traductions: Theorie der Funktionen einer reellen Veränderlichen. Berlin: Akademie-Verlag, 1954; Theory of functions of a real variable, vol. 1. New York: Frederick Ungar Publishing Co.

  • Radó Tibor. (1928) Sur un problème relatif à un théorème de Vitali. Fundamenta Math. 11: 228–229

    MATH  Google Scholar 

  • Royden Halsey L. (1988) Real analysis. 3e édition. Macmillan, New-York

    Google Scholar 

  • Scheeffer Ludwig. (1884–85) Zur Theorie der stetigen Funktionen einer reellen Veränderlichen b). Acta Math. 5: 279–296

    Article  MathSciNet  Google Scholar 

  • Sierpiński Wacław. (1923) Démonstration élémentaire du théorème sur la densité des ensembles. Fundamenta Math. 4: 167–171

    MATH  Google Scholar 

  • Souslin Mikhail Y. (1917) Sur une définition des ensembles mesurables B sans nombres transfinis. Comptes Rendus Acad. Sci. Paris 164: 88–91

    Google Scholar 

  • Stein Elias M. (1993) Harmonic analysis. Princeton University Press, Princeton Mathematical Series, 43. Princeton

    MATH  Google Scholar 

  • Vitali Giuseppe. (1905) Sulle funzioni integrali. Atti della Reale Accademia delle Scienze di Torino 40: 1021–1034

    MATH  Google Scholar 

  • Vitali Giuseppe. (1907–08) Sui gruppi di punti e sulle funzioni di variabili reali. Atti della Reale Accademia delle Scienze di Torino 43: 229–246

    Google Scholar 

  • Vitali Giuseppe. (1984) Opere sull’analisi reale e complessa. Florence, Edizioni Cremonese

    Google Scholar 

  • Wheeden Richard L., Antoni Zygmund. (1977) Measure and integral. Marcel Dekker, New York

    MATH  Google Scholar 

  • Zajíček Luděk. (2005) On σ-porous sets in abstract spaces. Abstract and Applied Analysis 2005(5): 509–534

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. UFR de Mathématiques, Université Paris-Diderot, Paris, France

    Bernard Maurey

  2. Projet Combinatoire et Optimisation, Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, Paris, France

    Jean-Pierre Tacchi

Authors
  1. Bernard Maurey
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jean-Pierre Tacchi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bernard Maurey.

Additional information

Communicated by: Jeremy Gray.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maurey, B., Tacchi, JP. Sur le théorème de recouvrement de Vitali. Arch. Hist. Exact Sci. 67, 81–118 (2013). https://doi.org/10.1007/s00407-012-0109-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00407-012-0109-6

Search

Navigation