| Course Description : | Lebesgue measure: outer measure, measurable sets and functions, Egoroff's theorem, Lusin's theorem, convergence in measure, the Lebesgue integral: the integral of a bounded function over a set of finite measure, the integral of a nonnegative function, the general Lebesgue integral, Riemann and Lebesgue integrals, differentiation: differentiation of monotone functions, functions of bounded variation, differentiation of an integral, absolute continuity, Lp classes: the Holder and Minkowski inequalities, completeness of Lp classes, the duals of Lp classes, Banach spaces: linear operators, the Hahn-Banach theorem and other basic results, Hilbert spaces. |