nLab Measure Theory

A book on measure theory by David H. Fremlin.

Website

Publisher: Torres Fremlin, Colchester. Later republished by Lulu.com.

1. 2004. 108+5 pp. ISBN: 0-9538129-0-1
2. 2003. 563+12 pp. ISBN: 0-9538129-2-8
3. 2004. 693+13 pp. ISBN: 0-9538129-3-6
4. 2006. I: 528 pp.; II: 439+19 pp. ISBN: 0-9538129-4-4
5. 2015. I: 329 pp. ISBN: 978-0-9538129-5-0; II: 411 pp. ISBN: 978-0-9538129-6-7

Volume 1. The Irreducible Minimum

1. Measure spaces?
2. Integration?
3. Complements

Appendix

Volume 2. Further topics in the general theory

1. Taxonomy of measure spaces
2. The fundamental theorem of calculus
3. The Radon-Nikodým theorem?
4. Function spaces
5. Product measures
6. Change of variable in the integral
7. Probability theory
8. Fourier analysis

Appendix

Volume 3. Measure Algebras

1. Boolean algebras
2. Measure algebras
3. Maharam’s theorem
4. Liftings
5. Riesz spaces
6. Function spaces
7. Linear operators between function spaces
8. Automorphism groups
9. Measurable algebras

Appendix

Volume 4. Topological Measure Spaces

1. Topologies and measures I
2. Descriptive set theory
3. Topologies and measures II
4. Topological groups?
5. Perfect measures, disintegrations? and processes
6. Pointwise compact sets of measurable functions
7. Geometric measure theory?
8. Gauge integrals?
9. Further topics

Appendix

Volume 5. Set-theoretic Measure Theory

1. Cardinal functions
2. Cardinal functions of measure theory
3. Topologies and measures III
4. Real-valued measurable cardinals?
5. Possible worlds
6. Choice and Determinacy

Appendix

Volume 6. Stochastic Calculus

1. The Riemann-sum integral
2. Martingales
3. Back to work
4. The fundamental theorem of martingales and the S-integral
5. Applications