This book grew out of my dual interest in the mathematics of integration theory and in the nature of its historical evolution. well known that modern theories of measure and integration have roots in the work of the French mathematician Henri Lebesgue. Although a relatively small amount of space is devoted to actually discussing Lebesgue's work, it represents the focal point of the entire book. objective has been to place Lebesgue's early work on integration theory (1901-10) within its proper historical context by relating it, on one hand, to the developments during the nineteenth century that
motivated it and gave it significance and, on the other hand, to the contributions made in this field by his contemporaries. It is my hope this volume will engender an appreciation for Lebesgue's genius balanced by an appreciation for the manner in which his work builds that of many other mathematicians.