Lebesgue Integral for Undergraduates

William Johnston is Professor of Mathematics at Butler University, Indiana. His publications include articles on operator theory and functional analysis, and the undergraduate textbooks A Transition to Advanced Mathematics: A Survey Course (with Alex McAllister) and An Introduction to Statistical Inference.

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

• PrefaceIntroductionChapter 1. Lebesgue Integrable FunctionsChapter 2. Lebesgue’s Integral Compared to Riemann’sChapter 3. Function SpacesChapter 4. Measure TheoryChapter 5. Hilbert Space OperatorsSolutions to Selected ProblemsBibliographyIndex