Introduction to Lebesgue Integration
by W W L Chen
Publisher: Macquarie University 1996
Number of pages: 75
An introduction to some of the basic ideas in Lebesgue integration with the minimal use of measure theory. Contents: the real numbers and countability, the Riemann integral, point sets, the Lebesgue integral, monotone convergence theorem, dominated convergence theorem, etc.
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by L. C. Young - Cambridge University Press
On the one hand, practically no knowledge is assumed; on the other hand, the ideas of Cauchy, Riemann, Darboux, Weierstrass, familiar to the reader who is acquainted with the elementary theory, are used as much as possible ...
by John K. Hunter - University of California Davis
These are some notes on introductory real analysis. They cover the properties of the real numbers, sequences and series of real numbers, limits of functions, continuity, differentiability, sequences and series of functions, and Riemann integration.
by Robert B. Ash - Institute of Electrical & Electronics Engineering
A text for a first course in real variables for students of engineering, physics, and economics, who need to know real analysis in order to cope with the professional literature. The subject matter is fundamental for more advanced mathematical work.
by John Franks - arXiv
My intent is to introduce the Lebesgue integral in a quick, and hopefully painless, way and then go on to investigate the standard convergence theorems and a brief introduction to the Hilbert space of L2 functions on the interval.