Mesures de Haar et -couple d’un groupoïde mesuré
We develop several methods of realization of scalar product and generalized moment problems. Constructions are made by use of a Hilbertian method or a fixed point method. The constructed solutions are rational fractions and exponentials of polynomials. They are connected to entropy maximization. We give the general form of the maximizing solution. We show how it is deduced from the maximizing solution of the algebraic moment problem.
We show that superreflexivity can be characterized in terms of bilipschitz embeddability of word hyperbolic groups.We compare characterizations of superrefiexivity in terms of diamond graphs and binary trees.We show that there exist sequences of series-parallel graphs of increasing topological complexitywhich admit uniformly bilipschitz embeddings into a Hilbert space, and thus do not characterize superrefiexivity.
An ellipse in R2 can be defined as the locus of points for which the sum of the Euclidean distances from the two foci is constant. In this paper we will look at the sets that are obtained by considering in the above definition distances induced by arbitrary norms.