Real Analysis I

3 credits · Undergraduate credit

Topics include: Lebesgue measure on the real line; measurable functions and integration on R; differentiation theory, fundamental theorem of calculus; function spaces, Lp (R), C(K), Holder and Minkowski inequalities, duality; general measure spaces, product measures, Fubini's Theorem; RadonNikodym Theorem, conditional expectation, signed measures, introduction to Fourier transforms.