Brownian local minima, random dense countable sets and random equivalence classes.

Tsirelson, Boris

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Standard representation of multivariate functions on a general probability space.

Janson, Svante (2009)

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Remarks on the Poisson Stochastic Process (II)

E. Marczewski (1953)

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Events of Borel Sets, Construction of Borel Sets and Random Variables for Stochastic Finance

Peter Jaeger (2014)

Formalized Mathematics

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We consider special events of Borel sets with the aim to prove, that the set of the irrational numbers is an event of the Borel sets. The set of the natural numbers, the set of the integer numbers and the set of the rational numbers are countable, so we can use the literature [10] (pp. 78-81) as a basis for the similar construction of the proof. Next we prove, that different sets can construct the Borel sets [16] (pp. 9-10). Literature [16] (pp. 9-10) and [11] (pp. 11-12) gives an overview,...