The content of differentiation and integration for single variable real functions will be extended to a more general context in this course. The topics of this course include measure theory, theory of Lebesgue integration, differentiation and integration theory for Lebesgue integral, as well as an introduction to Hilbert spaces.

CILO-1: Demonstrate the measure theory, measurable functions, and related properties. CILO-2: Dmonstrate the Lebesgue measure, and Lebesgue integrable functions, as well as Fubini’s theorem. CILO-3: Apply the differentiation and integration theory about Lebesgue integrable functions. CILO-4: Apply Hilbert spaces and related properties.