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Kies de Nederlandse taal
Course module: 201800321
201800321
Measure and Probability
Course info
Course module201800321
Credits (ECTS)5
Course typeCourse
Language of instructionEnglish
Contact persondr.ir. W.R.W. Scheinhardt
E-mailw.r.w.scheinhardt@utwente.nl
Lecturer(s)
Lecturer
S.P.R. Baas
Examiner
dr.ir. W.R.W. Scheinhardt
Contactperson for the course
dr.ir. W.R.W. Scheinhardt
Academic year2022
Starting block
1A
Application procedureYou apply via OSIRIS Student
Registration using OSIRISYes
Aims
After finishing the course, the student should
  • know what a measure is;
  • be aware of the problem of measurability of sets and be able to indicate its solution;
  • be able to discuss integrability of a function with respect to a measure;
  • know that probability theory is based on measure theory;
  • be able to identify notions from probability theory with notions from measure theory an integration theory;
  • understand basic concepts of convergence and be able to apply convergence theorems.
Content
The course is an introduction into measure and integration theory, with special attention to the fundamental role of this theory in probability. Contents: measure, Lebesgue measure, measure space, probability space, measurable function, stochastic variable, integral, Lebesgue integral, integrable function, expectation, product measure, Radon-Nikodym theorem, limit theorems.
Assumed previous knowledge
Necessary: basic calculus, set theory and probability theory
Participating study
Master Applied Mathematics
Required materials
Book
M. Capinski and E. Kopp, "Measure, Integral and Probability", Second edition, Corr 2nd printing, ISBN 978-1-85233-781-0
Recommended materials
-
Instructional modes
Lecture

Tutorial

Tests
Written exam

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Kies de Nederlandse taal