MATH4MI Measure and Integration
For many purposes in modern analysis the Riemann integral is inadequate. One of its biggest drawbacks being that the interchange of point-wise limits of function sequences and their integrals is only possible under rather restrictive conditions. This course introduces a modern theory of integration of real-valued functions via measure theory. One of the advantages of this approach is that it immediately provides a mathematical foundation for probability theory. In fact, throughout the course, we will discuss probabilistic interpretations and notations of the concepts we develop. Topics include sigma algebras, outer measures, Caratheodory’s Extension Theorem, construction of measures (in particular the Lebesgue measure on the real line), measurable functions and their integrals, convergence theorems and function spaces.
MATH201 with MATH301 strongly recommended
Petru A. Cioica-Licht (Room 212, phone 479 7783, email: email@example.com)
Start: Wednesday, March 1st, 3-5 pm.
Then, twice a week until week seven of the semester:
- Mondays, 9-11 am and Wednesday, 3-5 pm.
All lectures take place in room MA240.
- R. L. Schilling, Measures, Integrals and Martingales, Cambridge University Press, 2005. In course reserve.
- D. L. Cohn, Measure Theory, Second Edition, Birkhäuser, 2013.
- N. V. Krylov, Introduction to the Theory of Dissufion Processes, American Mathematical Society, 1995.
- W. Rudin, Real and Complex Analysis, McGraw-Hill Series in Higher Mathematics, McGraw-Hill, New York, 1974.
- M. E. Munroe, Measure and Integration, Addison-Wesley Publishing Company, Inc., 1953.
- G. B. Folland, Real Analysis, 2nd. Ed., Wiley, 1999.
Short weekly assignments
Your final mark F in the paper will be calculated according to this formula:
F = min(100, max(E, 0.4E + 0.6min(A, 125)))
- E is the Exam mark
- A is the Assignments mark
and all quantities are expressed as percentages.
Students must abide by the University’s Academic Integrity Policy
Academic endeavours at the University of Otago are built upon an essential commitment to academic integrity.
The two most common forms of academic misconduct are plagiarism and unauthorised collaboration.
Academic misconduct: Plagiarism
Plagiarism is defined as:
- Copying or paraphrasing another person’s work and presenting it as your own.
- Being party to someone else’s plagiarism by letting them copy your work or helping them to copy the work of someone else without acknowledgement.
- Using your own work in another situation, such as for the assessment of a different paper or program, without indicating the source.
- Plagiarism can be unintentional or intentional. Even if it is unintentional, it is still considered to be plagiarism.
All students have a responsibility to be aware of acceptable academic practice in relation to the use of material prepared by others and are expected to take all steps reasonably necessary to ensure no breach of acceptable academic practice occurs. You should also be aware that plagiarism is easy to detect and the University has policies in place to deal with it.
Academic misconduct: Unauthorised Collaboration
Unauthorised Collaboration occurs when you work with, or share work with, others on an assessment which is designed as a task for individuals and in which individual answers are required. This form does not include assessment tasks where students are required or permitted to present their results as collaborative work. Nor does it preclude collaborative effort in research or study for assignments, tests or examinations; but unless it is explicitly stated otherwise, each student’s answers should be in their own words. If you are not sure if collaboration is allowed, check with your lecturer.