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Bernoulli sequences and Borel measurability in ( 0 , 1 )

Petr Veselý (1993)

Commentationes Mathematicae Universitatis Carolinae

The necessary and sufficient condition for a function f : ( 0 , 1 ) [ 0 , 1 ] to be Borel measurable (given by Theorem stated below) provides a technique to prove (in Corollary 2) the existence of a Borel measurable map H : { 0 , 1 } { 0 , 1 } such that ( H ( X p ) ) = ( X 1 / 2 ) holds for each p ( 0 , 1 ) , where X p = ( X 1 p , X 2 p , ... ) denotes Bernoulli sequence of random variables with P [ X i p = 1 ] = p .

Between logic and probability.

Ton Sales (1994)

Mathware and Soft Computing

Logic and Probability, as theories, have been developed quite independently and, with a few exceptions (like Boole's), have largely ignored each other. And nevertheless they share a lot of similarities, as well a considerable common ground. The exploration of the shared concepts and their mathematical treatment and unification is here attempted following the lead of illustrious researchers (Reichenbach, Carnap, Popper, Gaifman, Scott & Krauss, Fenstad, Miller, David Lewis, Stalnaker, Hintikka...

Caracterización axiomática para la varianza.

María Angeles Gil Alvarez (1983)

Trabajos de Estadística e Investigación Operativa

En el artículo ([7]), M. Martín propone dos caracterizaciones axiomáticas para la varianza sugiriendo la posibilidad de caracterizarla de forma más intuitiva como una medida de incertidumbre que tenga en cuenta el soporte de la probabilidad, además del valor de ésta.El presente trabajo está dedicado a establecer una caracterización en tal sentido, siguiendo la línea de la axiomática de D. K. Faddeyew para la entropía de Shannon y de la axiomática propuesta en ([3]) para la medida definida en ([2]).Queremos...

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