MA 222A: Topics in Measure Theory

Credits: 3:0


Prerequisite courses: MA 219, MA 200, MA 222.

The aim is to treat certain topics which are just a tad too advanced to be included in a first course in measure and integration theory, but are not too specialized and are useful to analysts in general. Main Topics:

  1. Fourier Transform; Riemann- Lebesgue lemma, L^2 theory.
  2. Convergence in Measure.
  3. Riesz Representation Theorem.
  4. Functions of Bounded Variations; Fundamental Theorem of Calculus for absolutely continuous functions.
  5. Hausdorff Measures, Isodiametric Inequality.
  6. Area, Co-area Formulas.

In addition to these, some extra topics will be covered, depending on the instructor and time.


Suggested books and references:

  1. Lawrence Craig Evans and Ronald F. Gariepy, Measure Theory and Fine Properties of Functions, Chapman and Hall/CRC, 2015.
  2. Francesco Maggi, Sets of Finite Perimeter and Geometric Variational Problems; An Introduction to Geometric Measure Theory, Cambridge University Press, 2012.
  3. Juha Heinonen, Lectures on Analysis on Metric Spaces, Springer, 2001.
  4. Piotr Hajlasz, Sobolev mappings, co-area formula and related topics

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Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 05 Dec 2025