The (sub/super)additivity assertion of Choquet

• Autorzy: Heinz König
• Języki publikacji: EN

Abstrakty

EN

The assertion in question comes from the short final section in Theory of capacities of Choquet (1953/54), in connection with his prototype of the subsequent Choquet integral. The problem was whether and when this operation is additive. Choquet had the much more abstract idea that all functionals in a certain wide class must be subadditive, and similarly for superadditivity. His treatment of this point was more like an outline, and his proof limited to a rather narrow special case. Thus the proper context and scope of the assertion has remained open. In this paper we present a counterexample which shows that the initial context has to be modified, and then in a new context we prove a comprehensive theorem which fulfils all the needs that have turned up so far.

Kategorie tematyczne

• 26D15: Inequalities for sums, series and integrals
• 28C05: Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
• 28C15: Set functions and measures on topological spaces (regularity of measures, etc.)
• 28A12: Contents, measures, outer measures, capacities
• 26A51: Convexity, generalizations
• 52A40: Inequalities and extremum problems
• 46G12: Measures and integration on abstract linear spaces
• 28A25: Integration with respect to measures and other set functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 157
• Numer: 2
• Strony: 171-197

Daty

wydano

2003

Twórcy

autor

Heinz König

• Fakultät für Mathematik und Informatik, Universität des Saarlandes, D-66041 Saarbrücken, Germany

Identyfikatory

DOI

10.4064/sm157-2-4