Unit I: Review of Riemann Integral, Riemann-Stieltjes Integral.
Unit II: Lebesgue Measure; Lebesgue Outer Measure; Lebesgue Measurable Sets.
Unit III: Measure on an arbitrary sigma -Algebra; Measurable Functions; Integral of a Simple Measurable Function; Integral of Positive Measurable Functions.
Unit IV: Lebesgue's Monotone Convergence Theorem; Integrability; Dominated Convergence Theorem; Lp - Spaces. Differentiation and Fundamental theorem for Lebesgue integration.
Unit V: Product measure; Statement of Fubini's theorem.
- Teacher: Anoop T V