Shift invariant measures and simple spectrum
We consider some descriptive properties of supports of shift invariant measures on under the assumption that the closed linear span (in ) of the co-ordinate functions on is all of .
Théorème de la limite centrale et convergence fonctionnelle vers un processus à accroissements indépendants : la méthode des martingales
Sets with doubleton sections, good sets and ergodic theory
A Borel subset of the unit square whose vertical and horizontal sections are two-point sets admits a natural group action. We exploit this to discuss some questions about Borel subsets of the unit square on which every function is a sum of functions of the coordinates. Connection with probability measures with prescribed marginals and some function algebra questions is discussed.
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