This graduate-level course in Real Analysis provides a rigorous and in-depth study of the fundamental concepts and theorems underlying real analysis. The course focuses on the structure of the real number system, measure theory, integration, and the foundational principles of functional analysis. Students will develop the ability to construct precise mathematical arguments, engage with abstract concepts, and apply advanced analytical techniques to solve complex problems.

CILO-1: Identify the difference between the Riemann integral and the Lebesgue integral, explain what a measurable set is, and provide examples of non-measurable sets. CILO-2: Apply measure-theoretic techniques to solve advanced problems in integration and functional analysis. CILO-3: Construct and critique formal mathematical proofs. CILO-4: Analyze and generalize classical results to higher dimensions and abstract settings.