Using minimal prerequisites, this book unlocks the power Lebesgue integral, accessible at a surprisingly early stage in the undergraduate curriculum.
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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.
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.
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