Nearly All Convex Bodies Are Smooth and Strictly Convex.
Necessary and Sufficient Conditions for the Measurability of Certain Sets of Closed Subsets.
Non-Baire unions in category bases.
Non-compact random generalized games and random quasi-variational inequalities.
Nonmeasurable algebraic sums of sets of reals
We present a theorem which generalizes some known theorems on the existence of nonmeasurable (in various senses) sets of the form X+Y. Some additional related questions concerning measure, category and the algebra of Borel sets are also studied.
Non-separable analytic spaces and measurability
Non-transitive points and porosity
We establish that for a fairly general class of topologically transitive dynamical systems, the set of non-transitive points is very small when the rate of transitivity is very high. The notion of smallness that we consider here is that of σ-porosity, and in particular we show that the set of non-transitive points is σ-porous for any subshift that is a factor of a transitive subshift of finite type, and for the tent map of [0,1]. The result extends to some finite-to-one factor systems. We also show...
Normal subgroups of measurable automorphisms
Norms on possibilities. II: More ccc ideals on .