Measure theory is the modern theory of integration, the method of assigning a ”size” to subsets of a universal set. It is more general, more powerful and more beautiful than the classical theory of Riemann integration. This course will be an introduction to abstract measure theory and the Lebesgue integral. We will begin by defining the Lebesgue integral, prove the main convergence theorems, and construct Lebesgue measure in Rn. Other topics include Lp- spaces, abstract measure spaces.

The course is offered as a core course for IMM (International Mathematics Masters) and is divided into 3 modules. Module 1 is taught by Dr. Charlene Kalle (Lieden University, Netherlands), Module 2 by Dr. Waqas Ali Azhar (LUMS, Pakistan) and Module 3 by TBA.