on the concept of countability, to which I would urge students and
instructors to devote some time, as countability plays an very crucial
role in the study of measure theory.
In Appendix B we construct Lebesgue measure and prove it has
the properties cited in Chapter 2. In Appendix C we construct a
Finally, at the website http://www.ams.org/bookpages/stml-48
we provide solutions to a few of the more challenging exercises. These
exercises are marked with a ( ) when they occur in the text.
This text grew out of notes I have used in teaching a one quarter
course on integration at the advanced undergraduate level. With
some selectivity of topics and well prepared students it should be
possible to cover all key concepts in a one semester course.