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4 - Integration

Published online by Cambridge University Press:  06 July 2010

R. M. Dudley
Affiliation:
Massachusetts Institute of Technology
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Publisher: Cambridge University Press
Print publication year: 2002

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References

Alexits, G. (1930). Über die Erweiterung einer Baireschen Funktion.Fund. Math. 15: 51–56CrossRefGoogle Scholar
Bledsoe, W. W., and Morse, Anthony P. (1955). Product measures.Trans. Amer. Math. Soc. 79: 173–215CrossRefGoogle Scholar
Daniell, Percy J. (1917–1918). A general form of integral.Ann. Math. 19: 279–294CrossRefGoogle Scholar
Dudley, R. M. (1971). On measurability over product spaces.Bull. Amer. Math. Soc. 77: 271–274CrossRefGoogle Scholar
Fatou, Pierre Joseph Louis (1906). Séries trigonométriques et séries de Taylor.Acta Math. 30: 335–400CrossRefGoogle Scholar
Friedman, Harvey (1980). A consistent Fubini-Tonelli theorem for nonmeasurable functions.Illinois J. Math. 24: 390–395Google Scholar
*Fubini, Guido (1907). Sugli integrali multipli. Rendiconti Accad. Nazionale dei Lincei (Rome) (Ser. 5) 16: 608–614
Halmos, Paul R. (1950). Measure Theory. Van Nostrand, Princeton. Repr. Springer, New York (1974)CrossRef
Hausdorff, Felix (1914) (see references to Chapter 1)
Hawkins, T. (1970). Lebesgue's Theory of Integration, Its Origins and Development. University of Wisconsin Press
Hörmander, Lars (1983). The Analysis of Linear Partial Differential Operators, I. Springer, Berlin
Kuratowski, C. [Kazimierz] (1933). Sur les théorèmes topologiques de la théorie des fonctions de variables réelles. Comptes Rendus Acad. Sci. Paris 197: 19–20
Kuratowski, C. [Kazimierz] (1966). Topology, vol. 1. Academic Press, New York
Lebesgue, Henri (1902). Intégrale, longueur, aire (thèse, Univ. Paris). Annali Mat. pura e appl. (Ser. 3) 7: 231–359. Also in Lebesgue (1972–1973) 2, pp. 11–154CrossRef
Lebesgue, Henri(1904). Leçcons sur l'intégration et la recherche des fonctions primitives. Paris
Lebesgue, Henri(1910). Sur l'intégration des fonctions discontinues.Ann. Scient. Ecole Normale Sup. (Ser. 3) 27: 361–450. Also in Lebesgue (1972–1973), 2, pp. 185–274CrossRefGoogle Scholar
Lebesgue, Henri(1972–1973). Oeuvres scientifiques. 5 vols. L'Enseignement Math., Inst. Math., Univ. Genève
Lehmann, Erich (1959). Testing Statistical Hypotheses. 2d ed. Wiley, New York (1986)
Levi, Beppo (1906). Sopra l'integrazione delle serie.Rend. Istituto Lombardo di Sci. e Lett. (Ser. 2) 39: 775–780Google Scholar
May, Kenneth O. (1966). Biographical sketch of Henri Lebesgue. In Lebesgue, H., Measure and the Integral, Ed. K. O. May, Holden-Day, San Francisco, transl. from La Mesure des grandeurs, Enseignement Math 31–34 (1933–1936), repub. as a Monographie (1956)
Medvedev, F. A. (1975). The work of Henri Lebesgue on the theory of functions (on the occasion of his centenary). Russian Math. Surveys 30, no. 4: 179–191. Transl. from Uspekhi Mat. Nauk 30, no. 4: 227–238CrossRef
Nathan, Henry (1971). Fatou, Pierre Joseph Louis. In Dictionary of Scientific Biography, 4, pp. 547–548. Scribner's, New York
Rudin, Walter (1976). Principles of Mathematical Analysis. 3d ed. McGraw-Hill, New York
Saks, Stanisław (1937). Theory of the Integral. 2d ed. English transl. by L. C. Young. Hafner, New York. Repr. corrected Dover, New York (1964)
Schwartz, Laurent (1966). Théorie des Distributions. 2d ed. Hermann, Paris
Shortt, R. M. (1983). The extension of measurable functions.Proc. Amer. Math. Soc. 87: 444–446CrossRefGoogle Scholar
Sierpiński, Wacław (1920). Sur un problème concernant les ensembles measurables superficiellement.Fundamenta Math. 1: 112–115CrossRefGoogle Scholar
Sierpiński, Wacław(1930). Sur l'extension des fonctions de Baire définies sur les ensembles linéaires quelconques.Fund. Math. 16: 81–89CrossRefGoogle Scholar
Stigler, Stephen M. (1973). Simon Newcomb, Percy Daniell, and the history of robust estimation 1885–1920.J. Amer. Statist. Assoc. 68: 872–879Google Scholar
Stone, Marshall Harvey (1948). Notes on integration, II. Proc. Nat. Acad. Sci. USA 34: 447–455CrossRef
Tonelli, Leonida (1909). Sull'integrazione per parti. Rendiconti Accad. Nazionale dei Lincei (Ser. 5) 18: 246–253. Reprinted in Tonelli, L., Opere Scelte (1960), 1, pp. 156–165. Edizioni Cremonese, Rome
*Vitali, Giuseppe (1904–05). Sulle funzioni integrali.Atti Accad. Sci. Torino 40: 1021–1034Google Scholar
*Vitali, Giuseppe(1907). Sull'integrazione per serie.Rend. Circolo Mat. Palermo 23: 137–155CrossRefGoogle Scholar
Zaanen, Adriaan C. (1958). Introduction to the Theory of Integration. North-Holland, Amsterdam

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  • Integration
  • R. M. Dudley, Massachusetts Institute of Technology
  • Book: Real Analysis and Probability
  • Online publication: 06 July 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511755347.005
Available formats
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  • Integration
  • R. M. Dudley, Massachusetts Institute of Technology
  • Book: Real Analysis and Probability
  • Online publication: 06 July 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511755347.005
Available formats
×

Save book to Google Drive

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  • Integration
  • R. M. Dudley, Massachusetts Institute of Technology
  • Book: Real Analysis and Probability
  • Online publication: 06 July 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511755347.005
Available formats
×