Théorèmes ergodiques pour des mesures diagonales
We consider sets in uniformly perfect metric spaces which are null for every doubling measure of the space or which have positive measure for all doubling measures. These sets are called thin and fat, respectively. In our main results, we give sufficient conditions for certain cut-out sets being thin or fat.
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...
We construct strictly ergodic 0-1 Toeplitz flows with pure point spectrum and irrational eigenvalues. It is also shown that the property of being regular is not a measure-theoretic invariant for strictly ergodic Toeplitz flows.
The goal of this paper is to provide foundations for a new way to classify and characterize fractals using methods of computational topology. The fractal dimension is a main characteristic of fractal-like objects, and has proved to be a very useful tool for applications. However, it does not fully characterize a fractal. We can obtain fractals with the same dimension that are quite different topologically. Motivated by techniques from shape theory and computational topology, we consider fractals...