@MISC{FINANCE2.MIZ,
  AUTHOR = {Jaeger, Peter},
  TITLE = {Events of Borel Sets, Construction of Borel Sets and
           Random Variables for Stochastic Finance},
  SECTION1 = {Events of Borel Sets},
  SECTION2 = {Construction of Borel Sets},
  SECTION3 = {Random Variables for Stochastic Finance in Discrete Time},
  DAY = {10},
  MONTH = {July},
  YEAR = {2014},
  ADDRESS1 = {Siegmund-Schacky Str. 18a, 80993 Munich, Germany},
  SUMMARY = {We consider special events of Borel-Sets with the aim to prove,
             that IRRAT is an Event of the Borel-Sets. NAT, INT and RAT are
             countable, so we can use the literature \cite{analysis1:2001}
             (p. 78-81) as a basis for the similar construction of the proof.
             Next we prove, that different sets can construct the Borel-Sets
             \cite{klenke:2006} (p. 9-10). The literatures \cite{klenke:2006}
             (p. 9-10) and \cite{georgii:2004} (p. 11-12) give an overview,
             that there exists some other sets for this construction. Last we
             define special functions as Random-Variables for Stochastic
             Finance in discrete time. The relevant functions are implemented
             in the Finance1-Article, see \cite{follmerschied:2004} (p. 4). The
             aim is to construct Events and Random-Variables, which can easily
             be used with a Probability-Measure. See as an example theorem
             RANDOM_3:10 and RANDOM_3:14 where a random-variable is used with a
             Probability-Measure. Then the formalization is more similar to the
             presentation used in the book \cite{follmerschied:2004}. }}

@book{georgii:2004,
author={Georgii, Hans-Otto},
title={Stochastik, Einf\"uhrung
  in die Wahrscheinlichkeitstheorie und Statistik},
edition={2},
publisher={deGruyter},
year={2004},
ADDRESS={Berlin}}

@book{klenke:2006,
author={Klenke, Achim},
title={Wahrscheinlichkeitstheorie},
publisher={Springer-Verlag},
year={2006},
ADDRESS={Berlin, Heidelberg}}

@book{follmerschied:2004,
  author={F\"ollmer, Hans and Schied, Alexander},
  title={Stochastic Finance: An Introduction in Discrete Time},
  edition={2nd},
  volume={27},
  series={Studies in Mathematics},
  publisher={de Gruyter},
  year={2004},
  ADDRESS={Berlin}}

@book{analysis1:2001,
  author={Forster, Otto},
  title={Analysis 1},
  edition={6th},
  publisher={Vieweg-Verlag},
  year={2001},
  ADDRESS={Braunschweig/Wiesbaden}}

