Maat en integratie (WISB 312)

Intended audience: third-year students

Book: Measures, Integrals and Martingales, R. Schilling.

Outline: sigma-algebras and measures, Dynkin classes, Lebesgue measure, integration, modes of convergence for measurable and integrable functions, inequalities, image measures and integrals, uniform integrability, martingales, Radon-Nikodym theorem.

Prerequisites: It is expected that you have knowledge of analysis at the level of the course Functies en Reeksen. Some knowledge of functional analysis and/or probability theory can also be helpful.

Belangrijke mededelingen:

Behandeld bij hoorcollege:

Opgaven werkcollege/huiswerk:

  • Week 6: 3.2, 3.4iii, 3.5, 3.9, 3.10 and 3.11.
  • Week 7: 3.12, 4.3, 4.6, 4.11, 4.13 plus steropgave 1
  • Week 8: 4.14, 4.15, 5.2, 5.4, 5.6, 5.8, 5.9, 5.10 plus steropgave 2
  • Week 9: 6.1, 6.2, 6.3, 6.4i, ii, 6.5, 6.7, 6.9 plus steropgave 3
  • Week 10: 7.3, 7.4, 7.5, 7.6, 7.8, 7.9 en 7.10 plus steropgave 4
  • Week 12: 7.11, 8.3, 8.9, 8.10, 8.11, 8.12, 8.13, 8.14, geen steropgave.
  • Week 13: geen werkcollege i.v.m. quiz.
  • Week 14: 8.15, 8.17, 8.18, 9.4, 9.5, 9.7, 9.8, 9.9, 9.11 plus steropgave 5
  • Week 15: 10.2, 10.3, 10.5, 10.6, 10.7, 10.8, 10.9 plus steropgave 6
  • Week 17: 10.10, 10.11, 10.12, 10.15 plus steropgave 7
  • Week 18: 11.2, 11.3, 11.4, 11.7, 11.11, 11.12 plus steropgave 8
  • Week 19: 11.13, 11.14, 11.15, 12.1, 12.2, 12.3, 12.6, 12.8, 12.9, 12.10 plus steropgave 9
  • Week 20: geen college en werkcollege i.v.m. hemelvaartsdag
  • Week 21: geen werkcollege i.v.m. quiz 2
  • Week 22: 12.12, 12.13, 12.14, 12.15, 12.17, 12.18, 12.20,13.4,13.5, 13.6, 13.7 (geen steropgave)
  • Week 23: 13.8, 13.9, 13.10, 13.11, 13.12, 14.1, 14.2 plus steropgave 10
  • Week 24: van de handout ¬®Final part of the course": opgaven RN1, RN2, CE1, CE2, SM1, SM2 en SM3; geen steropgave

    Exams

    Determination of final grade: based on final exam, two quizzes and homework.

    Complete solutions of previous finals:

    Complete solutions of previous quizzes:

    Homework arrangement: