Introduction to the abstract measure theory and integration, including the following topics: Lebesgue measure and Lebesgue integral, Lp-spaces, convergence theorems, differentiation of measures, product measures (Fubini's theorem), abstract measures, Radon-Nikodym theorem, probabilistic language.
Lernziel
Basic acquaintance with the theory of measure and integration, in particular, Lebesgue's measure and integral.
Literatur
1. Lecture notes by Professor Michael Struwe (Link) 2. L. Evans and R.F. Gariepy "Measure theory and fine properties of functions" 3. Walter Rudin "Real and complex analysis" 4. R. Bartle The elements of Integration and Lebesgue Measure 5. P. Cannarsa & T. D'Aprile: Lecture notes on Measure Theory and Functional Analysis. Link
Leistungskontrolle
Information zur Leistungskontrolle (gültig bis die Lerneinheit neu gelesen wird)