Science/Engineering Modern theories of integration: H Kestelman (0486605728)

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Modern theories of integration: H Kestelman

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"The book is intended primarily for students who have covered the ground of G. H. Hardy' s Pure Mathematics. The account of the Lebesgue integral which is developed in this book follows the lines of C. Carathéodory 's Vorlesungen über réelle Funktionen • • • ." The following list of contents gives an adequate idea of the material contained in the book; the numerals are chapter numbers: I, Sets of points; II , Riemann integration; III , Lebesgue measure; IV, Sets of ordinates and measurable functions; V, Lebesgue integral of a non-negative function; VI, Lebesgue integrals of functions which are sometimes negative; VII , Functions of a single variable; VIII , Evaluation of double integrals; IX, Extensions of the Lebesgue integral; X, Fourier series. Chapter IX contains a simplified treatment of the Denjoy integral due to Romanovski . The exposition is rather detailed, but the title of the book appears to the reviewer somewhat misleading inasmuch as Stieltjes integrals and integration in abstract spaces are not even mentioned.

J. D. TAMARKIN

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