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Global Dependency Measure for Sets of Random Elements: “The Italian Problem” and Some Consequences

  • Jordan Stoyanov
Part of the Trends in Mathematics book series (TM)

Abstract

We suggest a detailed analysis of the classical independence/dependence properties for finite sets of random events or variables. All possible combinations of random elements are considered as a configuration obeying a hierarchical property. We define a function called a Dependency Measure taking values in the interval [0, 1] (0 corresponds to mutually independent sets; 1 corresponds to totally dependent sets) and serving as a global measure of the amount of dependency which is contained in the whole set of random elements. This leads to “The Italian Problem” about the existence of a probability model and a set of random elements with any prescribed independence/dependence structure. Some consequences and nonstandard illustrative examples are given. Related properties such as exchangeability and association are also discussed.

Keywords

Random Event Random Vector Probability Space Dependency Measure Sample Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Jordan Stoyanov
    • 1
  1. 1.Instituto de MatematicsUniversidade Federal do Rio de JaneiroRio de JaneiroBrasil

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