Bi- convex sets.
Boundaries of a Convex Set and Interpolation Sets.
Bounded Extensions and Characterizations of C(X).
Boundedness and continuity of additive and convex functionals.
Calculating norms in the spaces and .
Caractérisation des simplexes par des propriétés portant sur les faces fermées et sur les ensembles compacts de points extremaux.
Cardinality of some convex sets and of their sets of extreme points
We show that the cardinality of a compact convex set W in a topological linear space X satisfies the condition that . We also establish some relations between the cardinality of W and that of extrW provided X is locally convex. Moreover, we deal with the cardinality of the convex set E(μ) of all quasi-measure extensions of a quasi-measure μ, defined on an algebra of sets, to a larger algebra of sets, and relate it to the cardinality of extrE(μ).
Characterizations of ultrabarrelledness and barrelledness involving the singularities of families of convex mappings.
Choquet simplexes whose set of extreme points is -analytic
We construct a Choquet simplex whose set of extreme points is -analytic, but is not a -Borel set. The set has the surprising property of being a set in its Stone-Cech compactification. It is hence an example of a set that is not absolute.
Choquet theory in metric spaces.
Choquetova teorie a Dirichletova úloha
Choquetsimplexe und nukleare Räume.
Closed convex hull of set of measurable functions, Riemann-measurable functions and measurability of translations
Let be a locally compact group. Let be the left translation in , given by . We characterize (undre a mild set-theoretical hypothesis) the functions such that the map from into is scalarly measurable (i.e. for , is measurable). We show that it is the case when is measurable for each character , and if is compact, if and only if is Riemann-measurable. We show that is Borel measurable if and only if is left uniformly continuous.Some of the measure-theoretic tools used there...
Compactness and extreme points of the set of quasi-measure extensions of a quasi-measure [Book]
Complex Strict Convexity of Certain Banach Spaces.
Concerning interior mapping theorem
Cônes asymptotes d'ensembles non convexes
Cones of Lower Semicontinuous Functions and a Characterisation of Finely Hyperharmonic Functions.
Continuous Position and Existence Sets.
Continuous version of the Choquet integral representation theorem
Let E be a locally convex topological Hausdorff space, K a nonempty compact convex subset of E, μ a regular Borel probability measure on E and γ > 0. We say that the measure μ γ-represents a point x ∈ K if for any f ∈ E*. In this paper a continuous version of the Choquet theorem is proved, namely, if P is a continuous multivalued mapping from a metric space T into the space of nonempty, bounded convex subsets of a Banach space X, then there exists a weak* continuous family of regular Borel...