The Lebesgue integral / J. C. Burkill

Auteur principal : Burkill, John Charles, 1900-1993, AuteurType de document : MonographieCollection : Cambridge tracts in mathematics and mathematical physics, 40Langue : anglais.Pays: Grande Bretagne.Éditeur : London : Cambridge University Press, 1961Description : 1 vol. (viii-87 p.) ; 22 cmISBN: 9780521043823; 9780608156972.ISSN: 0068-6824.Bibliographie : Bibliogr..Sujet MSC : 26Axx, Real functions - Functions of one variable
26A42, Real functions - Functions of one variable, Integrals of Riemann, Stieltjes and Lebesgue type
26B15, Real functions - Functions of several variables, Integration: length, area, volume
En-ligne : Zentralblatt | MathSciNet
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The author states: "My aim is to give an account of the theory of integration due to Lebesgue in a form which may appeal to those who have no wish to plumb the depths of the theory of real functions. There is no novelty of treatment in this tract; the presentation is essentially that of Lebesgue himself. The groundwork in analysis and calculus with which the reader is assumed to be acquainted is, roughly, what is in Hardy's A course of pure mathematics [Cambridge Univ. Press, 1908].'' The author's treatment of measure and integration is similar in terminology, notation, approach, and scope to that in Titchmarsh's The theory of functions [Oxford, 1932]. The book contains the definition of the Lebesgue integral as the measure of the ordinate set; a brief treatment of multiple integrals, including Fubini's theorem; a chapter on the Lebesgue-Stieltjes integral for functions defined on the line; exercises with hints and solutions; and no bibliography and few references to the literature. (MathSciNet)


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