The Inclusion-Exclusion Principle for IF-States

Document Type: Research Paper

Authors

1 Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, Iowa 52242-1419, USA

2 Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovskeho 40, Banska Bystrica, Slovakia

Abstract

Applying two definitions of the union of IF-events, P. Grzegorzewski gave two generalizations of the inclusion-exclusion principle for IF-events.
In this paper we prove an inclusion-exclusion principle for IF-states based on a method which can also be used to prove Grzegorzewski's inclusion-exclusion principle for probabilities on IF-events.
Finally, we give some applications of this principle by extending some results regarding the classical probabilities to the case of the IF-states.

Keywords


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