The measure-theoretical approach to -adic probability theory
The return time theorem fails on infinite measure-preserving systems
The support of when the supports of and are given
The weak Radon-Nikodym property
The Zero-one law for Products of Internal *-finitely Additive Probabiltty Spaces
Theorems on lower semicontinuity and relaxation for integrands with fast growth.
Totally coherent set-valued probability assessments
We introduce the concept of total coherence of a set-valued probability assessment on a family of conditional events. In particular we give sufficient and necessary conditions of total coherence in the case of interval-valued probability assessments. Some relevant cases in which the set-valued probability assessment is represented by the unitary hypercube are also considered.
Translation invariance and finite additivity in a probability measure on the natural numbers.
Two classes of measures
Two dimensional probabilities with a given conditional structure
A properly measurable set (where are Polish spaces and is the space of Borel probability measures on ) is considered. Given a probability distribution the paper treats the problem of the existence of -valued random vector for which and -almost surely that possesses moreover some other properties such as “ has the maximal possible support” or “’s are extremal...
Two Kinds of Invariance of Full Conditional Probabilities
Let G be a group acting on Ω and ℱ a G-invariant algebra of subsets of Ω. A full conditional probability on ℱ is a function P: ℱ × (ℱ∖{∅}) → [0,1] satisfying the obvious axioms (with only finite additivity). It is weakly G-invariant provided that P(gA|gB) = P(A|B) for all g ∈ G and A,B ∈ ℱ, and strongly G-invariant provided that P(gA|B) = P(A|B) whenever g ∈ G and A ∪ gA ⊆ B. Armstrong (1989) claimed that weak and strong invariance are equivalent, but we shall show that this is false and that weak...
Ultralogics and probability models.
Un contre-exemple touchant à l'indépendance
Un point de priorité
Una aplicación de la teoría de la utilidad de Von Neumann a la probabilidad subjetiva.
En este artículo se da una condición necesaria y suficiente para la existencia y unicidad de una probabilidad subjetiva, finitamente aditiva, que concuerda con una probabilidad comparativa definida en una cierta clase de sucesos asociada al espacio paramétrico objeto de la inferencia.Nuestra constribución no evita tener que postular la relación de probabilidad comparativa en una clase mayor que la que es objeto de nuestro estudio pues exige la introducción de un espacio auxiliar que es el intervalo...
Uncertainty principle and joint distributions of observables
Une remarque sur la construction de noyaux
Une remarque sur le lemme de Borel-Cantelli
Uniqueness and approximate computation of optimal incomplete transportation plans
For α∈(0, 1) an α-trimming, P∗, of a probability P is a new probability obtained by re-weighting the probability of any Borel set, B, according to a positive weight function, f≤1/(1−α), in the way P∗(B)=∫Bf(x)P(dx). If P, Q are probability measures on euclidean space, we consider the problem of obtaining the best L2-Wasserstein approximation between: (a) a fixed probability and trimmed versions of the other; (b) trimmed versions of both probabilities. These best trimmed approximations naturally...
Upgrading Probability via Fractions of Events
The influence of “Grundbegriffe” by A. N. Kolmogorov (published in 1933) on education in the area of probability and its impact on research in stochastics cannot be overestimated. We would like to point out three aspects of the classical probability theory “calling for“ an upgrade: (i) classical random events are black-and-white (Boolean); (ii) classical random variables do not model quantum phenomena; (iii) basic maps (probability measures and observables – dual maps to random variables) have very...