This is a great introduction to integration theory, and probably the only book that is suitable for (1) a one semester course, and (2) a wide audience. The topics presented in this book are the main concepts ("work horse material") of integration and measure. I highly recommend this book as an introduction or tag along book for mathematicians (analysts), and as a primary book to learn the material for students in economics, electrical engineering, and statistics.
Author(s): Robert G. Bartle
Edition: 1
Publisher: Wiley-Interscience
Year: 1995
Language: English
Pages: 191
Contents......Page 7
The Elements of Integration......Page 11
1. Introduction......Page 13
2. Measurable Functions......Page 18
3. Measures......Page 31
4. The Integral......Page 39
5. Integrable Functions......Page 53
6. The Lebesgue Spaces L_p......Page 64
7. Modes of Convergence......Page 77
8. Decomposition of Measures......Page 92
9. Generation of Measures......Page 108
10. Product Measures......Page 125
The Elements of Lebesgue Measure......Page 137
11. Volumes of Cells and Intervals......Page 139
12. The Outer Measure......Page 143
13. Measurable Sets......Page 151
14. Examples of Measurable Sets......Page 161
15. Approximation of Measurable Sets......Page 167
16. Additivity and Nonadditivity......Page 173
17. Nonmeasurable and Non-Borel Sets......Page 177
References......Page 187
Index......Page 189
