Une notion générale de convergence faible pour des fonctions croissantes d'ensemble
Uniformly Regular sets of Measures on Completely Regular Spaces
Uniqueness of measure extensions in Banach spaces
Let X be a Banach space, a norming set and (X,B) the topology on X of pointwise convergence on B. We study the following question: given two (non-negative, countably additive and finite) measures μ₁ and μ₂ on Baire(X,w) which coincide on Baire(X,(X,B)), does it follow that μ₁ = μ₂? It turns out that this is not true in general, although the answer is affirmative provided that both μ₁ and μ₂ are convexly τ-additive (e.g. when X has the Pettis Integral Property). For a Banach space Y not containing...
Universally measurable spaces: an invariance theorem and diverse characterizations
Upper envelopes of inner premeasures
The paper resumes one of the themes initiated in the final sections of the celebrated “Theory of Capacities” of Choquet 1953-54. It aims at comprehensive versions in the spirit of the author’s recent work in measure and integration.