This book provides an elementary, self-contained presentation of the integration processes developed by Lebesgue, Denjoy, Perron, and Henstock. The Lebesgue integral and its essential properties are first developed in detail. The other three integrals are all generalizations of the Lebesgue integral that satisfy the ideal version of the Fundamental Theorem of Calculus: if $F$ is differentiable on the interval $[a,b]$, then $F'$ is integrable on $[a,b]$ and $\int_a^b F'= F(b) - F(a)$. One of the book's unique features is ...
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This book provides an elementary, self-contained presentation of the integration processes developed by Lebesgue, Denjoy, Perron, and Henstock. The Lebesgue integral and its essential properties are first developed in detail. The other three integrals are all generalizations of the Lebesgue integral that satisfy the ideal version of the Fundamental Theorem of Calculus: if $F$ is differentiable on the interval $[a,b]$, then $F'$ is integrable on $[a,b]$ and $\int_a^b F'= F(b) - F(a)$. One of the book's unique features is that the Denjoy, Perron, and Henstock integrals are each developed fully and carefully from their corresponding definitions.The last part of the book is devoted to integration processes which satisfy a theorem analogous to the Fundamental Theorem, in which $F$ is approximately differentiable. This part of this book is preceded by a detailed study of the approximate derivative and ends with some open questions. This book contains over 230 exercises (with solutions) that illustrate and expand the material in the text. It would be an excellent textbook for first-year graduate students who have background in real analysis.
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Add this copy of The Integrals of Lebesgue, Denjoy, Perron, and Henstock to cart. $45.00, very good condition, Sold by Moe's Books rated 5.0 out of 5 stars, ships from Berkeley, CA, UNITED STATES, published 1994 by American Mathematical Society.
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Fine with no dust jacket. 0821838059. Original blue silverstamped cloth. With diagrams. Slight shelfwear. VOLUME 4 ONLY; Graduate Studies In Mathematics; 18x25.6x2.7 cm; xi, 395 pages.
Add this copy of The Integrals of Lebesgue, Denjoy, Perron, and Henstock to cart. $74.25, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 1994 by American Mathematical Society.
Add this copy of The Integrals of Lebesgue, Denjoy, Perron, and Henstock to cart. $112.48, new condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 1994 by American Mathematical Society.