Real number system, open and closed sets. Lebesgue measure theory. Measurable functions. Lebesgue integration theory. Normed linear spaces. Inner products. Convergence and completeness. Orthonormal basis. Continuous linear functionals and dual spaces.

CILO-1: Understand the properties of Lebesgue measure and Lebesgue integral. CILO-2: Understand Lebesgue measure, measurable set, measurable function, Lebesgue integral. CILO-3: Understand the difference between Lebesgue integral and Riemann integral. CILO-4: Be able to solve some problems related to Lebesgue measure and Lebesgue integral. CILO-5: Understand the basics of Hilbert Spaces.