Measure Theory

National University of Ireland, Galway

Course Description

  • Course Name

    Measure Theory

  • Host University

    National University of Ireland, Galway

  • Location

    Galway, Ireland

  • Area of Study

    Mathematics

  • Language Level

    Taught In English

  • Prerequisites

    Enrollment of visiting students is subject to the agreement of the Head of Discipline and will depend upon the student's academic background in the relevent subject area.

  • Course Level Recommendations

    Upper

    ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

    Hours & Credits

  • ECTS Credits

    5
  • Recommended U.S. Semester Credits
    2
  • Recommended U.S. Quarter Units
    3
  • Overview

    Examinations for this course occuring during the summer.

    * The Lebesgue integral: the deficiencies of the Riemann integral, Lebesgue measure, measurable functions, the Lebesgue integral
    * Convergence theorems, functions of bounded variation and absolutely continuous functions, Vitali's Covering Theorem, integration and differentiation
    * General measure and integration theory: outer measures, measures, measurable functions, modes of convergence
    * Functional analysis: normed vector spaces and inner product spaces, bounded linear mappings, linear functionals and the dual space, the classical Banach spaces and their duals, Hilbert spaces, orthogonal decomposition, orthonormal bases, Fourier series

    Texts

    * H.L. Royden, "Real Analysis" (Collier Macmillan)
    * E. Kreyszig, "Introductory Functional Analysis with Applications" (Wiley)

    References

    * R.G.Bartle, "The Elements of Integration" (Wiley)
    * A. Brown & C. Pearcey, Introduction to Operator Theory, Vol I (Springer)
    * E. Hewitt & K. Stromberg, "Real and Abstract Analysis" (Springer)
    * M. Spiegel, "Real Variables" (Schaum Outline)
    * W. Rudin, "Functional Analysis" (McGraw Hill)
    * W. Rudin, "Real and Complex Analysis" (McGraw Hill)
    * M. Schechter, "Principles of Functional Analysis" (Academic Press)
    * N. Young, "An Introduction to Hilbert Spaces" (Cambridge)

Course Disclaimer

Courses and course hours of instruction are subject to change.

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.

ECTS (European Credit Transfer and Accumulation System) credits are converted to semester credits/quarter units differently among U.S. universities. Students should confirm the conversion scale used at their home university when determining credit transfer.

Please reference fall and spring course lists as not all courses are taught during both semesters.

Please note that some courses with locals have recommended prerequisite courses. It is the student's responsibility to consult any recommended prerequisites prior to enrolling in their course.