Caractérisation des mesures qui intègrent toutes les fonctions réelles mesurables
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).
Compactness and extreme points of the set of quasi-measure extensions of a quasi-measure [Book]
Compactness and other questions in spaces of uniform measures
Completeness of the space of separable measures in the Kantorovich-Rubinshtein metric.
Cone-constrained linear equations in Banach spaces.
Continuity Properties of the Extension of a Locally Lipschitz Continuous Map to the Space of Probability Measures.
Convergence diffuse d'une suite de fonctions
Countable tightness in the spaces of regular probability measures
We prove that if K is a compact space and the space P(K × K) of regular probability measures on K × K has countable tightness in its weak* topology, then L₁(μ) is separable for every μ ∈ P(K). It has been known that such a result is a consequence of Martin's axiom MA(ω₁). Our theorem has several consequences; in particular, it generalizes a theorem due to Bourgain and Todorčević on measures on Rosenthal compacta.
Criterios de convergencia de medidas de conjuntos Riemann integrables.