A note on de Finetti's lower probabilities and belief measures

Abstract

De Finetti has introduced lower and upper probabilities as boundary set functions when extending a fixed probability from an atomic algebra to an atomic superalgebra. We discuss the relationship of de Finetti’s lower and upper probabilities with belief and plausibility measures, and also investigate the order of their additivity. Finally, two open problems are formulated.

Keywords

• belief measure
• k-additivity
• lower probability
• plausibility measure
• upper probability