Lecture Winter Term 2019/2020

An Introduction to Measure Theoretic Probability



Alexander Lindner

Class Teacher:

David Berger

Type: MSc. Finance elective course


There is a block course in the week before the regular start of the lecture period, so from 7th of Oct. until 11th of Oct.

The schedule is as follow:

  • Mon., 07.10.2019: Lecture: 8:15-11:45 He18, 1.20. Exercise Class: 16:15-17:45 He18, 1.20.
  • Tue.,  08.10.2019: Lecture: 8:15-11:45 He18, 1.20
  • Wed., 09.10.2019: Lecture: 8:15-11:45 He18, 1.20.
  • Fri.,    11.10.2019:  Lecture: 8:15-11:45 He18, 1.20Exercise Class: 16:15-17:45 He18, 1.20.
Time and Venue: Schedule of the course from 14th of October until 6th of January:
  • Lecture: Monday, 08:15-09:45, He18 - 1.20
  • First Lecture: 14/10/2019
  • Exercise class: Wednesday, 08:15-09:45, He22 - E.04
  • First Exercise class: 16/10/2019

Final Exam:

written and closed exam of 90 minutes on Monday, 27th of January 2020, 08:15-09:45, He18 - 1.20.

Retake of the exam on Thursday, 5th of March 2020, 10:00-11:30.

To participate in the written exam, you have to register at campusonline.uni-ulm.de until Wednesday, 22th of January 2020.


Analysis I+II and Linear Algebra I.


This course covers the basic but nevertheless relevant (especially for Financial Mathematics I) topics of probability theory in a measure-theoretic approach.

Specific topics are

  • Definition and properties of measure and the Lebesgue integral.
  • The fundamentals of probability: probability space, random variables, conditional expectation, modes of convergence, convolutions and characteristic functions, central limit theorem.
  • An introduction to statistics: simple random sampling, introduction to estimation techniques.


Available in the library.
  • H. Bauer, Measure and Integration Theory, De Gruyter Studies in Mathematics, 2011.
  • H. Bauer, Probability Theory, De Gruyter Studies in Mathematics, 2011.
  • P. Billingsley, Probability and Measure, Wiley, 2012.
  • W. Rudin, Real and Complex Analysis, McGraw-Hill International Editions, 1987.
  • J. Jacod & P. Protter, Probability Essentials, 2nd edition, Springer, 2004.
  • E. Kopp, J. Malczak & T. Zastawniak, Probability for Finance, Cambridge University Press, 2014.
  • R. Leadbetter, S. Cambanis, V. Pipiras, A Basic Course in Measure and Probability, Cambridge University Press, 2014.
  • A. N. Shiryaev, Probability, 2nd edition, Springer, 1995.
  • D. Williams, Probability with Martingales, Cambridge University Press, 1991.

Exercise sheets:


Lecture notes:


Additional Material:

Refresher in Probability 1

Refresher in Probability 2