Measure and the integral.
Subtitle: Edited with a biographical essay by Kenneth O. May
By: Edited with a biographical essay by Kenneth O. May.
Contributors: May, Kenneth O. 1915- ed.; Lebesgue, Henri Léon, 1875-1941.; Lebesgue, Henri Léon, 1875-1941.
Edition: First edition
Series: The Mathesis series
Publisher: Holden-Day
Published: 1966
Place of publication: San Francisco, USA
Language: eng
Format: Hardcover
Number of pages: 210
Copyright date: ©1966
Subjects: Measure theory.; Integrals, Generalized.; Lebesgue integral.
Description: This book contains translations of two essays by Henri Lebesgue. The first, which takes up most of the book, is entitled "Measure of Magnitudes" and was published seri- ally in l'Enseignement Mathematique during the years 1931-1935. With the French school system primarily in mind, Lebesgue discusses possible ways to present the subject on the elementary, secondary and collegiate levels "in as simple and specific a manner as possi- ble but without sacrificing logical rigor." The first four chapters deal with the notions of whole numbers, length and real numbers, area and volume. Much of what Lebesgue sug- gests could be used profitably in a high school geometry course. Chapter V deals with curve length and surface area and contains some interesting remarks relating to Lebes- gue's own work on the problem of defining the area of a surface. In the final two chapters the notion of a set function is introduced and used as the context for an elegant treatment of differentiation and integration along the lines found in Buck's Advanced Calculits. The essay concludes with a lucid discussion of oriented integrals and volumes.
Notes: Bibliography: p. 6-7. Bibliographical footnotes.
Contains translations of Measure of magnitudes, originally published in l'Enseignement mathématique, 1931-1935, and of Development of the integral concept, first published in Matematisk tidsskrift B, 1926.
Table of contents: title: -- Comparisons of collections: whole numbers; title: -- Lengths, numbers; title: -- Areas; title: -- Volumes; title: -- Lengths of curves, areas of surfaces; title: -- Measurable magnitudes; title: -- Integration and differentiation; title: -- Conclusions