The (sub/super)additivity assertion of Choquet

Heinz König. "The (sub/super)additivity assertion of Choquet." Studia Mathematica 157.2 (2003): 171-197. <http://eudml.org/doc/285337>.

@article{HeinzKönig2003,
abstract = {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.},
author = {Heinz König},
journal = {Studia Mathematica},
keywords = {(sub/super)additive functionals; convex functions; Choquet integral; Stonean function classes; Stonean and truncable functionals; (sub/super)modular functionals; Danull-Stone representation; Riesz representation},
language = {eng},
number = {2},
pages = {171-197},
title = {The (sub/super)additivity assertion of Choquet},
url = {http://eudml.org/doc/285337},
volume = {157},
year = {2003},
}

TY - JOUR
AU - Heinz König
TI - The (sub/super)additivity assertion of Choquet
JO - Studia Mathematica
PY - 2003
VL - 157
IS - 2
SP - 171
EP - 197
AB - 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.
LA - eng
KW - (sub/super)additive functionals; convex functions; Choquet integral; Stonean function classes; Stonean and truncable functionals; (sub/super)modular functionals; Danull-Stone representation; Riesz representation
UR - http://eudml.org/doc/285337
ER -