The Elements of Integration and Lebesgue Measure

The Elements of Integration and Lebesgue Measure

Contents

1. Introduction

2. Measurable Functions

3. Measures

4. The Integral

5. Integrable Functions

6. The Lebesgue Spaces L_p

7. Modes of Convergence

8. Decomposition of Measures

9. Generation of Measures

10. Product Measures

11. Volumes of Cells and Intervals

12. The Outer Measure

13. Measurable Sets

14. Examples of Measurable Sets

15. Approximation of Measurable Sets

16. Additivity and Nonadditivity

17. Nonmeasurable and Non-Borel Sets

References

Index

People often ask me to recommend a good introduction to measure theory. More often than not, I recommend Bartle. It is a short, highly readable book with plenty of simple exercises that build your skills without taxing your patience. If you are unfamiliar with real analysis—point-set topology, convergence of sequences of functions, delta-epsilon proofs—you will want to read Apsotol (1974) first.

For related books, see sections:

Math - Calculus/Analysis

Math - Measure Theory

Math - Probability

Math - Stochastic Calculus


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