Search results for "Set function"
showing 7 items of 7 documents
On the admissibility of the space L_{0}(A, X) of vector-valued measurable functions
2013
We prove the admissibility of the space L_0(A,X) of vector-valued measurable functions determined by real-valued finitely additive set functions defined on algebras of sets.
Rearrangement and convergence in spaces of measurable functions
2007
We prove that the convergence of a sequence of functions in the space of measurable functions, with respect to the topology of convergence in measure, implies the convergence -almost everywhere ( denotes the Lebesgue measure) of the sequence of rearrangements. We obtain nonexpansivity of rearrangement on the space , and also on Orlicz spaces with respect to a finitely additive extended real-valued set function. In the space and in the space , of finite elements of an Orlicz space of a -additive set function, we introduce some parameters which estimate the Hausdorff measure of noncompactness. We obtain some relations involving these parameters when passing from a bounded set of , or , to th…
On a multiplication and a theory of integration for belief and plausibility functions
1987
Abstract Belief and plausibility functions have been introduced as generalizations of probability measures, which abandon the axiom of additivity. It turns out that elementwise multiplication is a binary operation on the set of belief functions. If the set functions of the type considered here are defined on a locally compact and separable space X , a theorem by Choquet ensures that they can be represented by a probability measure on the space containing the closed subsets of X , the so-called basic probability assignment. This is basic for defining two new types of integrals. One of them may be used to measure the degree of non-additivity of the belief or plausibility function. The other o…
A BASIC MODEL OF INTERACTING SUBJECTS
1980
Abstract In studying the problem of interaction between subjects, an approach which allows us to define in an unambiguous way the concepts of symmetrical, complementary and parallel interaction is proposed. This approach makes use of a point of view within which it is possible to develop a rational model based only on some fundamental elements of set theory and mathematical logic The model allows us to develop a probabilistic theory of change, the representation basis of which is furnished by the 16 basic set functions. The functions represent operations on two partially overlapping sets, which will be called the “worlds”, of interacting subjects.. Both an interaction test that allows a “me…
Team Theory and Person-by-Person Optimization with Binary Decisions
2012
In this paper, we extend the notion of person-by-person (pbp) optimization to binary decision spaces. The novelty of our approach is the adaptation to a dynamic team context of notions borrowed from the pseudo-boolean optimization field as completely local-global or unimodal functions and submodularity. We also generalize the concept of pbp optimization to the case where groups of $m$ decisions makers make joint decisions sequentially, which we refer to as $m$b$m$ optimization. The main contribution is a description of sufficient conditions, verifiable in polynomial time, under which a pbp or an $m$b$m$ optimization algorithm converges to the team-optimum. As a second contribution, we prese…
A Model of Multiproduct Price Competition
1997
Abstract We provide a simple model of price competition in a multiproduct oligopoly market. The products are of general nature. We find that a pure strategy equilibrium exists and every equilibrium consumption maximizes the total social surplus. Consumers are characterized by a set function which determines their willingness to pay for every subset of products. If this function is convex, the set of equilibrium prices coincides with the core of a cooperative game generated by this set function and the firms extract total industry surplus. If it is concave, the only equilibrium price of a product is its marginal contribution to the consumer's total willingness to pay. Journal of Economic Lit…
A CHARACTERIZATION OF THE WEAK RADON–NIKODÝM PROPERTY BY FINITELY ADDITIVE INTERVAL FUNCTIONS
2009
AbstractA characterization of Banach spaces possessing the weak Radon–Nikodým property is given in terms of finitely additive interval functions. Due to that characterization several Banach space valued set functions that are only finitely additive can be represented as integrals.