On Probability Function On Pseudo-Boolean Algebra
On probability of first order formulas in a given model
On products of admissible liftings and densities.
On pseudo-random sequences and their relation to a class of stochastical laws
On shifting iterated convolutions I
On some contributions to quantum structures by fuzzy sets
It is well known that the fuzzy sets theory can be successfully used in quantum models ([5, 26]). In this paper we give first a review of recent development in the probability theory on tribes and their generalizations – multivalued (MV)-algebras. Secondly we show some applications of the described method to develop probability theory on IF-events.
On some properties of the Lüroth-type alternating series representations for real numbers.
On the amount of information resulting from empirical and theoretical knowledge.
We present a mathematical model allowing formally define the concepts of empirical and theoretical knowledge. The model consists of a finite set P of predicates and a probability space (Ω, S, P) over a finite set Ω called ontology which consists of objects ω for which the predicates π ∈ P are either valid (π(ω) = 1) or not valid (π(ω) = 0). Since this is a first step in this area, our approach is as simple as possible, but still nontrivial, as it is demonstrated by examples. More realistic approach...
On the approximation properties of Bernstein polynomials via probabilistic tools.
On the Borel-Cantelli Lemma and moments
We present some extensions of the Borel-Cantelli Lemma in terms of moments. Our result can be viewed as a new improvement to the Borel-Cantelli Lemma. Our proofs are based on the expansion of moments of some partial sums by using Stirling numbers. We also give a comment concerning the results of Petrov V.V., A generalization of the Borel-Cantelli Lemma, Statist. Probab. Lett. 67 (2004), no. 3, 233–239.
On the convergence of operators
On the dimension of an irrigable measure
On the evaluation of the degree of progress to goal in a multi-purpose self-organization process
On the existence of conditional density functions
On the existence of disintegrations
On the expected value of vector lattice-valued random variables
On the Gaussian random matrix ensembles with additional symmetry conditions.
On the Inequality ...pi f(pi) > piif(qi).
On the need to adapt de Finetti's probability interpretation to QM
von Neumann's reliance on the von Mises frequentist interpretation is discussed and compared with the Dutchbook approach proposed by de Finetti.
On the Principle of Equivalence of Sparre Andersen.