This book is an introduction to measure theory and Lebesgue integration and it is dedicated to advanced undergraduate and graduate students in mathematics. Informed by history, attempting to the motivations, uncertainties, and difficulties surrounding the key concepts of the field, this book is devoted to explain the answers to the five historical questions that changed the nature of analysis forever and that led to the development of measure theory and Lebesgue integration. Moreover, this is a story of any contributions by many members of a large community of mathematicians working on different pieces of the puzzle in the late nineteenth, early twentieth century.

Reviewer:

Octavian Lipovan (Timişoara)