MATH 5010

Measure & Integration

Lec 01 selected

Lebesgue's theory of measure and integration. The topics include: sigma-algebras, measures, construction of measures, Lebesgue measure on the real line, measurable functions, the Lebesgue integral and convergence theorems, Lp spaces, signed and complex measures, decomposition of measures and the Lebesgue-Radon-Nikodym theorem, product measures and the Fubini-Tonelli theorem.

Sections

Lecture

From the syllabus

From the Fall 2023 syllabus by Suresh Eswarathasan. Fall 2026 is taught by Fraser A., so details may differ. Open the PDF

Grading

40%Biweekly homework assignments
10%Biweekly journals4010 journals cover the previous two weeks; 5010 journals cover each day
25%In-class midtermTentatively October 27, 2023
25%Final examDuring the predetermined exam period; date TBD

Textbook

  • Real Analysis: Measure Theory, Integration, and Hilbert Spaces, E. Stein and R. Shakarchi

Course rules

Late homework
Contact the instructor for a one-on-one discussion; extensions or later submissions may be arranged for legitimate excuses.
Missed midterm
The final exam will count for 50% of the grade.
Collaboration
Submit individual homework and name any students you collaborated with.
AI use
Indicate on submitted assignments if you used ChatGPT or another AI.

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