Kolmogorov complexity leads to a representation theorem for idempotent probabilities (σ-maxitive measures)

  • Authors:

  • Vladik Kreinovich;Luc Longpré

  • Affiliations:

  • University of Texas at El Paso, El Paso, TX;University of Texas at El Paso, El Paso, TX

  • Venue:
  • ACM SIGACT News
  • Year:
  • 2005

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Abstract

In many application areas, it is important to consider maxitive measures (idempotent probabilities), i.e., mappings m for which m(A ∪ B) = max(m(A), m(B)). In his papers, J. H. Lutz has used Kolmogorov complexity to show that for constructively defined sets A, one maxitive measure - fractal dimension - can be represented as m(A) = sup f(x). We show that a similar representation is possible for an arbitrary maxitive measure.