Fundamentals of Analysis for EE - part I
closed sets, open sets, Cauchy sequences, completeness, compactness, Theorem of Heine–Borel, continuity and uniform continuity of functions, uniform convergence of sequences of functions.
algebras, measures and outer measures, measurable sets, discrete measure spaces, Lebesgue measure on the real line, measurable functions, Lebesgue integral, dominated convergence theorem, $L_p$-spaces as complete normed spaces. Time-permitting: signed measures and absolute continuity of measures and the Radon-Nykodim theorem.
- University course catalogue: