Introduction to Lebesgue Integration
by W W L Chen
Publisher: Macquarie University 1996
Number of pages: 187
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 Richard F. Bass - CreateSpace
Nearly every Ph.D. student in mathematics needs to take a preliminary or qualifying examination in real analysis. This book provides the necessary tools to pass such an examination. The author presents the material in as clear a fashion as possible.
by Larry Clifton - arXiv
This is a detailed introduction to the real number system from a categorical perspective. We begin with the categorical definition of the natural numbers, review the Eudoxus theory of ratios, and then define the positive real numbers categorically.
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 Krzysztof Ciesielski - Heldermann Verlag
This text surveys the recent results that concern real functions whose statements involve the use of set theory. The choice of the topics follows the author's personal interest in the subject. Most of the results are left without the proofs.