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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 .
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.
[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.
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]
As a C. L. E. Moore instructor, Rudin taught the real analysis course at MIT in the 1951–1952 academic year. [2] [3] After he commented to W. T. Martin, who served as a consulting editor for McGraw Hill, that there were no textbooks covering the course material in a satisfactory manner, Martin suggested Rudin write one himself.
The logical status of the property depends on the construction of the real numbers used: in the synthetic approach, the property is usually taken as an axiom for the real numbers (see least upper bound axiom); in a constructive approach, the property must be proved as a theorem, either directly from the construction or as a consequence of some ...
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 ...