The probability of observing xt at time t, given past observations x1...xt−1 can be computed with Bayes’ rule if the true generating distribution μ of the sequences x1x2x3... is known. If μ is unknown, but known to belong to a class M one can base ones prediction on the Bayes mix ξ defined as a weighted sum of distributions ν ∈M. Various convergence results of the mixture posterior ξt to the tr...

Triangular norms in the study of probabilistic metric spaces as a special kind of associative functions defined on the unit interval. These functions have found applications in many areas since then. In this study, we present new methods for constructing triangular norms and triangular conorms on an arbitrary bounded lattice under some constraints. Also, we give some illustrative examples for t...

We consider a vector field whose coefficients are functions of bounded variation, with a bounded divergence. We prove the uniqueness of continuous solutions for the Cauchy problem.

Let X be a Banach space and (Ω,Σ) be a measure space. We provide a characterization of sequences in the space of X-valued countably additive measures on (Ω,Σ) of bounded variation that generates complemented copies of l1. As application, we prove that if a dual Banach space E∗ has Pe lczyński’s property (V*) then so does the space of E∗-valued countably additive measures with the variation norm...