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A geometry on the space of probabilities (II). Projective spaces and exponential families.

Henryk Gzyl, Lázaro Recht (2006)

Revista Matemática Iberoamericana

In this note we continue a theme taken up in part I, see [Gzyl and Recht: The geometry on the class of probabilities (I). The finite dimensional case. Rev. Mat. Iberoamericana 22 (2006), 545-558], namely to provide a geometric interpretation of exponential families as end points of geodesics of a non-metric connection in a function space. For that we characterize the space of probability densities as a projective space in the class of strictly positive functions, and these will be regarded as a...

A projective central limit theorem and interacting Fock space representation for the limit process

Vitonofrio Crismale (2007)

Banach Center Publications

Accardi et al. proved a central limit theorem, based on the notion of projective independence. In this note we use the symmetric projective independence to present a new version of that result, where the limiting process is perturbed by the insertion of suitable test functions. Moreover we give a representation of the limit process in 1-mode type interacting Fock space.

Conditional states and joint distributions on MV-algebras

Martin Kalina, Oľga Nánásiová (2006)


In this paper we construct conditional states on semi-simple MV-algebras. We show that these conditional states are not given uniquely. By using them we construct the joint probability distributions and discuss the properties of these distributions. We show that the independence is not symmetric.

Contractions on probabilistic metric spaces: examples and counterexamples.

Berthold Schweizer, Howard Sherwood, Robert M. Tardiff (1988)


The notion of a contraction mapping for a probabilistic metric space recently introduced by T. L. Hicks is compared with the notion previously introduced by V. L. Sehgal and A. T. Bharucha-Reid. By means of appropriate examples, it is shown that these two notions are independent. It is further shown that every Hick's contraction on a PM space (S,F,tW) is an ordinary metric contraction with respect to a naturally defined metric on that space; and it is again pointed out that, in Menger spaces under...

Didactical note: probabilistic conditionality in a Boolean algebra.

Enric Trillas, Claudi Alsina, Settimo Termini (1996)

Mathware and Soft Computing

This note deals with two logical topics and concerns Boolean Algebras from an elementary point of view. First we consider the class of operations on a Boolean Algebra that can be used for modelling If-then propositions. These operations, or Conditionals, are characterized under the hypothesis that they only obey to the Modus Ponens-Inequality, and it is shown that only six of them are boolean two-place functions. Is the Conditional Probability the Probability of a Conditional? This problem will...

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