13D081MI - Measure and Integration

Course specification
Course title Measure and Integration
Acronym 13D081MI
Study programme Electrical Engineering and Computing
Module Applied Mathematics
Type of study doctoral studies
Lecturer (for classes)
    Lecturer/Associate (for practice)
      Lecturer/Associate (for OTC)
        ESPB 9.0 Status elective
        Condition Mathematics on the level of compulsory courses at ETF as well as familiarity with elements of probability theory.
        The goal The course presents a generalization of methods of calculus in one and more variables which are based on concepts of length, area and volume. The goal of the course is learnig this classical theory and its applications and gaining knowledge of properties and techniques related to abstract measure theory and integration theory, Laplace and Fourier transform etc.
        The outcome Student will be able to read and understand literature where the concepts of measure and integrations are used and applied in mathematical models. Student will be able to use these concepts and acquired knowledge in his/her own research and to use it in the process of solving applied problems.
        Contents of lectures Jordan measure. Lebesgue measure and integral. Lebesgue-Stieltjes integral and its properties. Abstract measure spaces. Types of convergence. Differentiation theorems. Lp spaces. Product measures. Infinite product spaces and Kolmogorov's extension theorem. Fourier and Laplace transform of measures, inversion and applications.
        Contents of exercises
        1. Terence Tao: An Introduction to Measure Theory, Graduate Studies in Mathematics, Vol. 126, American Mathematical Society 2011.
        2. Leonard Richardson: Measure and Integration - A Concise Introduction to Real Analysis, John Wiley and sons, 2009.
        3. Walter Rudin: Functional analysis. Second edition. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York 1991.
        4. M. Carter, B. van Brunt, "The Lebesgue-Stieltjes Integral: A Practical Introduction",Springer 2000.
        Number of hours per week during the semester/trimester/year
        Lectures Exercises OTC Study and Research Other classes
        Methods of teaching Mentoring, consultations,seminar. Individual programs for each student, depending on his/her background and the area of doctorate. Textbooks are used in selected parts, depending on individual needs. If there is a sufficient number of students, classical lectures will be held, with the main textbook cited first in the list.
        Knowledge score (maximum points 100)
        Pre obligations Points Final exam Points
        Activites during lectures Test paper 70
        Practical lessons Oral examination
        Seminars 30