Riemann-Stieltjes Integral, measure and Lebesgue Integral, Convergence of infinite series of functions, Fourier series, some Hilbert space theory. Tests of convergence of infinite series. Convergence of infinite sequences and series of functions.
Some approximation theorems.
B. Generalizations of the Riemann Integral. Measurable sets, measurable functions, and the Lebesgue Integral. Convergence in measure. C. Hilbert spaces. Some other examples and applications of Hilbert spaces .