Bengt Ringnér Centre for Mathematical Sciences, dept. of Mathematical Statistics Lund University with Lund Institute of Technology

Interests

• Mathematics and probability

  General 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".

• Mathematical logic

  • Gödel's incompleteness theorem

Links

• Kolmogorov's "Grundbegriffe der Wahrscheinlichkeitsrechnung" (1933), translated to English, at www.mathematik.com.
• www.mathematik.com.

Address: Centre for Mathematical Sciences, Box 118, SE-22100, Lund, Sweden
Internal postal system: HS6