A Radical Approach to Lebesque's Theory of Integration

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 Riemanns definition of the integral and then follows the efforts of those who wrestled with the difficulties inherent in it until Lebesgue finally broke with Riemanns definition. With his new way of understanding integration Lebesgue opened the door to fresh and productive approaches to the previously intractable problems of analysis.