Summary and Info
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.
More About the Author
Russell T. Gordon (born 3 July 1936, died November 2013) was an American painter and printmaker. He moved to Montreal in 1973 where he was a visiting professor then faculty member at Concordia University until he retired in 1998.
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