Advanced Real Analysis I, 7.5 credits

About the course

The course covers measure theory, integration and functional analysis, integration of measurable functions (Lebesgue integrals), convergence theorems, product measure, Fubini's theorem, Banach spaces including the LP spaces and fundamental theorems on linear operators and functionals. Applications are found in Fourier analysis, ergodic theory, probability theory, Sobolev spaces and partial differential equations.

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