Researcher, affiliated with the university
Mathematics and probabilityGeneral overview with links to proofs hard to extract from the literature:
- Fundamental Theorem, aka Kolmogorov's existence theorem for stochastic processes.
- Extension Theorem for measures done through integration. It also contains a proof of the Stone-Daniell representation theorem.
- Prohorov's theorem. It is most conveniently proved through the Stone-Daniell theorem.
- Fubini's theorem on iterated integration of double integrals.
- The formula E(g(X)) = ∫ g(x)dF_X(x), called "the law of the unconscious statistician".
- Kolmogorov's "Grundbegriffe der Wahrscheinlichkeitsrechnung" (1933), translated to English, at www.mathematik.com.