Sets of extended uniqueness and -porosity
We show that there exists a closed non--porous set of extended uniqueness. We also give a new proof of Lyons’ theorem, which shows that the class of -sets is not large in .
We show that there exists a closed non--porous set of extended uniqueness. We also give a new proof of Lyons’ theorem, which shows that the class of -sets is not large in .
We study the ``smallness'' of the set of non-hypercyclic vectors for some classical hypercyclic operators.
If X is a compact metric space of dimension n, then K(X), the n- dimensional kernel of X, is the union of all n-dimensional Cantor manifolds in X. Aleksandrov raised the problem of what the descriptive complexity of K(X) could be. A straightforward analysis shows that if X is an n-dimensional complete separable metric space, then K(X) is a or PCA set. We show (a) there is an n-dimensional continuum X in for which K(X) is a complete set. In particular, ; K(X) is coanalytic but is not an analytic...
We show that for a wide class of σ-algebras 𝓐, indicatrices of 𝓐-measurable functions admit the same characterization as indicatrices of Lebesgue-measurable functions. In particular, this applies to functions measurable in the sense of Marczewski.