Convex analysis for sets of local martingales measures
Convex cones and convex sets
Convex sets and Harnack inequality
Convexity and Reflexivity
Convexity of measures in certain convex cones in vector space ...-algebras.
Convexity preserving summability matrices.
Correction to the paper: Sets invariant under projections onto one dimensional subspaces
Densité de l’espace des fonctions affines continues sur un convexe compact dans l’espace d’une mesure maximale
Description of all regular cones in a Hilbert space.
Descriptive properties of elements of biduals of Banach spaces
If E is a Banach space, any element x** in its bidual E** is an affine function on the dual unit ball that might possess a variety of descriptive properties with respect to the weak* topology. We prove several results showing that descriptive properties of x** are quite often determined by the behaviour of x** on the set of extreme points of , generalizing thus results of J. Saint Raymond and F. Jellett. We also prove a result on the relation between Baire classes and intrinsic Baire classes...
Diameter-preserving maps on various classes of function spaces
Under some mild assumptions, non-linear diameter-preserving bijections between (vector-valued) function spaces are characterized with the help of a well-known theorem of Ulam and Mazur. A necessary and sufficient condition for the existence of a diameter-preserving bijection between function spaces in the complex scalar case is derived, and a complete description of such maps is given in several important cases.
Dilated Sets and Characterizations of Simplexes.
Directional derivates and almost everywhere differentiability of biconvex and concave-convex operators.
Distances to spaces of affine Baire-one functions
Let E be a Banach space and let and denote the space of all Baire-one and affine Baire-one functions on the dual unit ball , respectively. We show that there exists a separable L₁-predual E such that there is no quantitative relation between and , where f is an affine function on . If the Banach space E satisfies some additional assumption, we prove the existence of some such dependence.
Drop property on locally convex spaces
A single technique provides short proofs of some results about drop properties on locally convex spaces. It is shown that the quasi drop property is equivalent to a drop property for countably closed sets. As a byproduct, we prove that the drop and quasi drop properties are separably determined.
Duality and integral representation for excessive measures.
Enlarging a subspace of C(X) without changing the Choquet boundary.
Epiconvergence and -subgradients of convex functions.
Épluchabilité et unicité du prédual
Existence and integral representation of regular extensions of measures
Let ℒ be a δ-lattice in a set X, and let ν be a measure on a sub-σ-algebra of σ(ℒ). It is shown that ν extends to an ℒ-regular measure on σ(ℒ) provided ν*|ℒ is σ-smooth at ∅ and ν*(L) = inf ν*(U)|X ∖ U ∈ ℒ, Usupset L for all L ∈ ℒ. Moreover, a Choquet type representation theorem is proved for the set of all such extensions.