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Historical Note

(Chapters II to V)

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(N.B. — The Roman numerals refer to the bibliography at the end of this note.)

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Bibliography

  1. L. Euler, Opera Omnia: De formulis integralibus duplicatis (1), v. XVII, Leipzig-Berlin (Teubner), 1915, pp. 289–315.

    Google Scholar 

  2. G. Lejeune-Dirichlet, Sur la convergence des séries trigonométriques qui servent à représenter une fonction arbitraire entre des limites données, J. de Crelle, 4 (1829), pp. 157–169 (= Werke, v. I, pp. 118–132, Berlin (G. Reimer ), 1889 ).

    Article  MATH  Google Scholar 

  3. B. Riemann, Gesammelte Mathematische Werke, 2nd. edn., Leipzig (Teubner), 1892.

    MATH  Google Scholar 

  4. G. Cantor, Gesammelte Abhandlungen, Berlin (Springer), 1932.

    Google Scholar 

  5. G. Peano, Applicazioni geometriche del calcolo infinitesimale, Turin, 1887.

    MATH  Google Scholar 

  6. C. Jordan, Cours d’Analyse, v. I, 2nd. edn., Paris (Gauthier- Villars), 1893.

    MATH  Google Scholar 

  7. C. Arzelà: a) Sulla integrabilità di una serie di funzioni, Rendic. Acc. dei Lincei, (4), 1 (1885), pp. 321–326; b) Sulla integrazione per serie, ibid., pp. 532–537 and 566–569.

    Google Scholar 

  8. T. Stieltjes, Recherches sur les fractions continues, Ann. Fac. Sci de Toulouse, 8 (1894), J. 1 to J. 122.

    MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  10. H. Lebesgue: a) Intégrale, longueur, aire, Annali di Mat., (3), 7 (1902), pp. 231–359; b) Leçons sur l’Intégration et la recherche des fonctions primitives, Paris (Gauthiers-Villars), 1904; c) Sur les séries trigonométriques, Ann. Ec. Norm. Sup., (3), 20 (1903), pp. 453–485; d) Sur l’intégration des fonctions discontinues, Ann. Éc. Norm. Sup., (3), 27 (1910), pp. 361–450.

    MathSciNet  Google Scholar 

  11. W. H. Young: a) On upper and lower integration, Proc. Lond. Math. Soc., (2), 2 (1905), pp. 52–66; b) A new method in the theory of integration, Proc. Lond. Math. Soc., (2), 9 (1911), pp. 15–50.

    Article  Google Scholar 

  12. G. Vitali: a) Una proprieta delle funzioni misurabili, R. Ist. Lombardo, Rendiconti, (2), 38 (1905), pp. 599–603;Sui gruppi di punti e sulle funzioni di variabili reali, Rendic. Acc. Sci. di Torino, 43 (1908), pp. 229–236.

    Google Scholar 

  13. E. Fischer, Sur la convergence en moyenne, C. R. Acad. Sci., 144 (1907), pp. 1022–1024.

    MATH  Google Scholar 

  14. G. Fubini, Sugli integrali multipli, Rendic. Acc. dei Lincei, (5), 16 (1907), pp. 608–614.

    Google Scholar 

  15. F. Riesz: a) Sur les systèmes orthogonaux de fonctions, C. R. Acad. Sci., 144 (1907), pp. 615–619; b) Untersuchungen über Systeme integrierbarer Funktionen, Math. Ann., 69 (1910), pp. 449–497; c) Sur certains systèmes singuliers d’équations intégrales, Ann. Éc. Norm. Sup., (3), 28 (1911), pp. 33–62; d) Sur quelques notions fondamentales dans la théorie générale des opérations linéaires, Ann. of Math., (2), 41 (1940), pp. 174–206.

    Google Scholar 

  16. D. Egoroff, Sur les suites de fonctions mesurables, C. R. Acad. Sci., 152 (1911), p. 244.

    MATH  Google Scholar 

  17. J. Radon, Theorie und Anwendungen der absolut additiven Mengenfunktionen, Sitzungsber. der math. naturwiss. Klasse der Akad. der Wiss. (Wien), 122, Abt. IIa (1913), pp. 1295–1438.

    Google Scholar 

  18. C. Carathéodory, Vorlesungen über reelle Funktionen, Leipzig-Berlin (Teubner), 1918.

    MATH  Google Scholar 

  19. P. J. Daniell, a) A general form of integral, Ann. of Math., (2), 19 (1918), pp. 279–294; b) Integrals in an infinite number of dimensions, Ann. of Math., (2), 20 (1919), pp. 281–288.

    MathSciNet  Google Scholar 

  20. O. Nikodym, Sur une généralisation des intégrales de M. J. Radon, Fund. Math., 15 (1930), pp. 131–179.

    MATH  Google Scholar 

  21. S. Bochner, Integration von Funktionen deren Werte die El-emente eines Vektorraumes sind, Fund. Math., 20 (1933), pp. 262–276.

    Google Scholar 

  22. J. von Neumann, On rings of operators. III, Ann. of Math., (2), 41 (1940), pp. 94–161.

    Article  MathSciNet  Google Scholar 

  23. A. Kolmogoroff, Grundbegriffe der Wahrscheinlichkeits-rechnung, Berlin (Springer), 1933.

    Google Scholar 

  24. S. SAKS, Theory ofthe integral, 2nd. edn., New York (Stechert), 1937.

    Google Scholar 

  25. A. Zygmund, Trigonometric series, Warsaw, 1935 (2nd. edn., Cambridge University Press, 1959 ).

    MATH  Google Scholar 

  26. L. Cesari, Surface area, Princeton, 1954.

    Google Scholar 

  27. L. H. Loomis, An introduction to abstract harmonic analysis, London-New York-Toronto (van Nostrand), 1953.

    MATH  Google Scholar 

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Bourbaki, N. (2004). Historical Note. In: Elements of Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59312-3_7

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  • DOI: https://doi.org/10.1007/978-3-642-59312-3_7

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