Kolmogorov Complexity Leads to a Representation Theorem for Idempotent Probabilities (Sigma-Maxitive Measures)

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Luc Longpre, The University of Texas at El PasoFollow

Publication Date

6-2005

Comments

UTEP-CS-05-20.

Published in ACM SIGACT News, 2005, Vol. 36, No. 3, pp. 107-112.

Abstract

In many application areas, it is important to consider maxitive measures (idempotent probabilities), i.e., mappings m for which m(A U 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): x in A}. We show that a similar representation is possible for an arbitrary maxitive measure.