Continuity properties of decomposable probability measures on euclidean spaces

Absolute Continuity and Singularity of Probability Measures in Functional Spaces

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Composition of Probability Measures on Finite Spaces

Decomposable models and Bayesian net­ works can be defined as sequences of oligo­ dimensional probability measures connected with opemtors of composition. The prelim­ inary results suggest that the probabilistic models allowing for effective computational procedures are represented by sequences pos­ sessing a special property; we shall call them perfect sequences. The present paper lays down th...

Coherent Risk Measures on General Probability Spaces

We extend the definition of coherent risk measures, as introduced by Artzner, Delbaen, Eber and Heath, to general probability spaces and we show how to define such measures on the space of all random variables. We also give examples that relates the theory of coherent risk measures to game theory and to distorted probability measures. The mathematics are based on the characterisation of closed ...

Continuity of Barycentric Coordinates in Euclidean Topological Spaces

For simplicity, we adopt the following rules: x denotes a set, n, m, k denote natural numbers, r denotes a real number, V denotes a real linear space, v, w denote vectors of V , A1 denotes a finite subset of V , and A2 denotes a finite affinely independent subset of V . One can prove the following propositions: (1) For all real-valued finite sequences f1, f2 and for every real number r holds (I...