The aim of this course is to provide a solid foundation in real analysis. The content includes set functions and elementary ring, extension of regular nonnegative additive set functions, Lebesgue measure zero sets and non-measurability, Lebesgue measurable functions, Lebesgue integrals, convergence theorem of Lebesgue integrals.

CILO-1: Analyze the properties of construction of Lebesgue measure. CILO-2: Explain the key ideas of the properties of measurable functions. CILO-3: Apply concepts of the Lebesgue integrals and its properties including convergence theorems.