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Interval Probability on Finite Sample Spaces

  • Kurt Weichselberger
Part of the Lecture Notes in Statistics book series (LNS, volume 109)

Abstract

In the seventies and early eighties theory of interval probability has gained very much from contributions of Peter Huber. The present article gives an outline of an approach aiming to establish unifying foundations of that theory. A system of axioms for interval probability is described generalizing Kolmogorov’s axioms for classical probability and distinguishing two types of interval probability. The first one (R-probability) is characterized by employing interval-limits which are not self-contradictory, while the interval-limits of the second (F-probability) fit exactly to the set of classical probabilities in accordance to these interval-limits (structure). The task of controlling whether an assignment of intervals to each random event of a finite sample space represents at least R-probability or even F-probability is done by means of Linear Programming. The possibility of characterizing R-probability by features of its structure is sketched. A thorough presentation of theory will be given in a forthcoming book by the author.

Key words and phrases

Interval probability axiomatic foundations of probability 

AMS 1991 subject classifications

Primary 60A05 

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Copyright information

© Springer-Verlag New York, Inc. 1996

Authors and Affiliations

  • Kurt Weichselberger
    • 1
  1. 1.Ludwig-Maximilians-Universität MünchenGermany

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