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Basic Real Analysis

Houshang H. Sohrab
Publisher: 
Birkhäuser
Publication Date: 
2014
Number of Pages: 
683
Format: 
Hardcover
Edition: 
2
Price: 
89.99
ISBN: 
9781493918409
Category: 
Textbook
[Reviewed by
Fernando Q. Gouvêa
, on
12/13/2014
]

See our review of the first edition. The most significant change in this edition is that the treatment of Lebesgue integration is now done in the more traditional way, with Lebesgue measure defined first and then the Lebesgue integral. The author says "I have come to believe that measure theory is a fundamental part of analysis and the sooner one learns it, the better."

Preface

Set Theory

Sequences and Series of Real Numbers

Limits of Functions

Topology of R and Continuity

Metric Spaces

The Derivative

The Riemann Integral

Sequences and Series of Functions

Normed and Function Spaces

Lebesgue Measure and Integral in R

More on Lebesgue Integral and Measure

General Measure and Probability

Appendix A: Construction of Real Numbers

Bibliography

Index.