MATH 481 : Real Analysis II

MATH 481 : Real Analysis II (E) 4 (3+1+0) credit hours Riemann Integrations: the definition, Darboux theorem, Riemann sums, the fundamental theorem. Sequences and series of functions: uniform convergence for the sequences and series of functions, power series. Lebesgue measure: Borel σ-algebra, outer measure, Lebesgue measurable sets, Properties of Lebesgue measure. Lebesgue integral: simple functions, measurable functions, definition of Lebesgue integral, Monotone convergence theorem, bounded convergence theorem, the relation between Lebesgue and Riemann integrals. Prerequisite : MATH 382