Lærebok/Text book:
Measures, Integrals and Martingales
by René L. Schilling, Cambridge University Press (2005), ISBN-13: 9780521615259
Pensum/Syllabus:
The syllabus this fall consists of Ch. 1-13, plus subsections 1, 2, 6-9 in Ch. 19, with the following exceptions :
- the proof of Thm 2.7
- the detailed proof of Thm 6.1 (only an understanding of the main lines is required)
- Lemma 8.13 and its proof
- the proof of Thm 11.8 ii)
- the proof of Thm 12.7
- Lemma 12.6, Thm 12.10, Lemma 12.13 and Thm 12.14, including their proofs
- Thm 13.10, Lemma 13.12, Cor. 13.13, Thm 13.14, including their proofs
- the proof of Thm 19.2.
All given exercises, including extra-exercises, are part of the syllabus.
Covered topics are described in the detailed teaching plan.
An alternative to chapter 2 about sets, functions and counting (from MAT4500) may be be found here .