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Rudin, Walter R. (1976) Principles of Mathematical Analysis, Third Edition, McGraw–Hill. See Theorem 7.13 on page 150 for the monotone decreasing case. Thomson, Brian S.; Bruckner, Judith B.; Bruckner, Andrew M. (2008) [2001]. Elementary Real Analysis. ClassicalRealAnalysis.com. ISBN 978-1-4348-4367-8
Robert Gardner Bartle (November 20, 1927 – September 18, 2003) was an American mathematician specializing in real analysis. He is known for writing the popular textbooks The Elements of Real Analysis (1964), The Elements of Integration (1966), and Introduction to Real Analysis (2011) with Donald R. Sherbert, published by John Wiley & Sons .
[3]: 30 William G. Bade and Robert G. Bartle were brought on as research assistants. [5] Dunford retired shortly after finishing the final volume. [3]: 30 Schwartz, however, went on to write similarly pathbreaking books in various other areas of mathematics. [1] [a] The book met with acclaim when published.
Known as Little Rudin, contains the basics of the Lebesgue theory, but does not treat material such as Fubini's theorem. Rudin, Walter (1966). Real and complex analysis. New York: McGraw-Hill Book Co. pp. xi+412. MR 0210528. Known as Big Rudin. A complete and careful presentation of the theory. Good presentation of the Riesz extension theorems.
Rudin's text was the first modern English text on classical real analysis, and its organization of topics has been frequently imitated. [1] In Chapter 1, he constructs the real and complex numbers and outlines their properties. (In the third edition, the Dedekind cut construction is sent to an appendix for pedagogical reasons.) Chapter 2 ...
Walter Rudin (May 2, 1921 – May 20, 2010 [2]) was an Austrian-American mathematician and professor of mathematics at the University of Wisconsin–Madison. [3]In addition to his contributions to complex and harmonic analysis, Rudin was known for his mathematical analysis textbooks: Principles of Mathematical Analysis, [4] Real and Complex Analysis, [5] and Functional Analysis. [6]
Bartle, Robert G.; Sherbert, Donald R. (2000). Introduction to Real Analysis (3rd ed.). New York City: John Wiley and Sons. ISBN 0-471-32148-6. Abbott, Stephen (2001). Understanding Analysis. Undergraduate Texts in Mathematics. New York: Springer Verlag. ISBN 0-387-95060-5. Rudin, Walter (1976). Principles of Mathematical Analysis. Walter Rudin ...
First we prove the theorem for (set of all real numbers), in which case the ordering on can be put to good use. Indeed, we have the following result: Indeed, we have the following result: Lemma : Every infinite sequence ( x n ) {\displaystyle (x_{n})} in R 1 {\displaystyle \mathbb {R} ^{1}} has an infinite monotone subsequence (a subsequence ...