Measure and the integral

The reader who expects to find Lebesgue's opinions on how to present the concepts of Lebesgue measure and integration will be disappointed by "Measure and Magnitudes." It is perhaps to compensate for this omission that the editor has appended a fifteen page expository article, "The Development of the Integral Concept," published by Lebesgue in 1926. Here we find a clear, non-technical introduction to the Lebesgue integral and its relation to the definitions of Cauchy and Riemann. This is followed by a brief discussion of the manner in which Lebesgue's definition was generalized by Radon and Denjoy. A short biographical sketch has been supplied by the editor together with a selected bibliography for those who would like to learn more about Lebesgue's life and work.