The Lebesgue Integral

An Elementary Approach

By: William Johnston

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Hardcover | 30 December 2015

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This text presents the Lebesgue integral at an accessible undergraduate level with surprisingly minimal prerequisites. Anyone who has mastered single-variable calculus concepts of limits, derivatives, and series can learn the material. The key to this success is the text's use of a method labeled the "Daniell-Riesz approach." The treatment is self-contained, and so the associated course, often offered as Real Analysis II, no longer needs Real Analysis I as a prerequisite. Additional curricular options then exist. Academic institutions can now offer a course on the integral (and function spaces) along with Complex Analysis and Real Analysis I, where completion of any one course enhances the other two. Students can enroll immediately after Calculus II, after a first course in mathematical proofs, or as a required course in function theory. Along with Vector Calculus and Probability Theory, this set of courses now provides a comprehensive undergraduate investigation into functions.

Industry Reviews

In 1902, modern function theory began when Henri Lebesgue described a new 'integral calculus.' His Lebesgue integral handles more functions than the traditional integral--so many more that mathematicians can study collections (spaces) of functions. For example, it defines a distance between any two functions in a space. This book describes these ideas in an elementary, accessible way. Anyone who has mastered calculus concepts of limits, derivatives, and series can enjoy the material. Unlike any other text, this book brings analysis research topics within reach of readers even just beginning to think about functions from a theoretical point of view." - Mathematical Reviews Clippings

"When I noticed the title of this book, I was curious to see if this subject actually could be made comprehensible to an undergraduate. It turns out that it really can be, via a path to the Lebesgue integral that is different from the one I took as a graduate student... I like books that try something new, offer a different perspective on things, and are carefully and clearly written. This one qualifies on all counts. This is a book, I think, that students will actually read, and even better, enjoy." - Mark Hunacek, MAA Reviews

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