The construction of a function given by moments. (La construction de quelque fonction par des moments donnés.)
The Existence of Measurable Approximating Maximums.
The Extension Problem for Measurable Positive Definite Functions.
The point of continuity property, neighbourhood assignments and filter convergences
We show that for some large classes of topological spaces X and any metric space (Z,d), the point of continuity property of any function f: X → (Z,d) is equivalent to the following condition: (*) For every ε > 0, there is a neighbourhood assignment of X such that d(f(x),f(y)) < ε whenever . We also give various descriptions of the filters ℱ on the integers ℕ for which (*) is satisfied by the ℱ-limit of any sequence of continuous functions from a topological space into a metric space.
The range of vector measures into Orlicz spaces
The strength of the projective Martin conjecture
We show that Martin’s conjecture on Π¹₁ functions uniformly -order preserving on a cone implies Π¹₁ Turing Determinacy over ZF + DC. In addition, it is also proved that for n ≥ 0, this conjecture for uniformly degree invariant functions is equivalent over ZFC to -Axiom of Determinacy. As a corollary, the consistency of the conjecture for uniformly degree invariant Π¹₁ functions implies the consistency of the existence of a Woodin cardinal.
The theory of -generators and some questions in analysis.
Theorems on lower semicontinuity and relaxation for integrands with fast growth.
Tightness, integral equicontinuity and compactness for evolution problems in Banach spaces
Compactness in the space , being a separable Banach space, has been deeply investigated by J.P. Aubin (1963), J.L. Lions (1961, 1969), J. Simon (1987), and, more recently, by J.M. Rakotoson and R. Temam (2001), who have provided various criteria for relative compactness, which turn out to be crucial tools in the existence proof of solutions to several abstract time dependent problems related to evolutionary PDEs. In the present paper, the problem is examined in view of Young measure theory: exploiting...
Towers of measurable functions
We formulate variants of the cardinals f, p and t in terms of families of measurable functions, in order to examine the effect upon these cardinals of adding one random real.
Typical measurable function in the topology of close approximation.