This lively introduction to measure theory and Lebesgue integration is
motivated by the historical questions that led to its development. The
author stresses the original purpose of the definitions and theorems,
highlighting the difficulties mathematicians encountered as these ideas
were refined. The story begins with Riemann's definition of the
integral, and then follows the efforts of those who wrestled with the
difficulties inherent in it, until Lebesgue finally broke with Riemann's
definition. With his new way of understanding integration, Lebesgue
opened the door to fresh and productive approaches to the previously
intractable problems of analysis.

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