Some combinatorial problems on the measurability of functions with respect to invariant extensions of the Lebesgue measure
Some combinatorial questions related to measure theory
Some comments on independent σ-algebras
Some complexity results in topology and analysis
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...
Some connections between Falconer's distance set conjecture and sets of Furstenburg type.
Some connections between measure, indiscernibility and representation of cuts
Some continuity and approximation properties of a countable iterated function system.
Some continuity and measurability results on spaces of measures.
Some dimensional results for a class of special homogeneous Moran sets
We construct a class of special homogeneous Moran sets, called -quasi homogeneous Cantor sets, and discuss their Hausdorff dimensions. By adjusting the value of , we constructively prove the intermediate value theorem for the homogeneous Moran set. Moreover, we obtain a sufficient condition for the Hausdorff dimension of homogeneous Moran sets to assume the minimum value, which expands earlier works.
Some examples of d-ideals and related Baire systems
Some extensions of an inequality of Vapnik and Chervonenkis.
Some full descriptive characterizations of the Henstock-Kurzweil integral in the Euclidean space
Using generalized absolute continuity, we characterize additive interval functions which are indefinite Henstock-Kurzweil integrals in the Euclidean space.
Some Functional Inequalities.
Some generic properties of concentration dimension of measure
Let be a compact quasi self-similar set in a complete metric space and let denote the space of all probability measures on , endowed with the Fortet-Mourier metric. We will show that for a typical (in the sense of Baire category) measure in the lower concentration dimension is equal to , while the upper concentration dimension is equal to the Hausdorff dimension of .
Some metric-singular properties of the graph of solutions of the one-dimensional -Laplacian.
Some operations related with translation
Some possible covers of measure zero sets
Some problems for measures on non-standard algebraic structures
Nell'ultimo ventennio tutta una serie di lavori è stata rivolta allo studio delle misure su strutture algebriche più generali delle algebre di Boole, come i poset e i reticoli ortomodulari, le effect algebras, le BCK-algebras. La teoria così ottenuta interessa l'analisi funzionale, il calcolo delle probabilità e la topologia, più recentemente la teoria delle decisioni. Si presentano alcuni risultati relativi a misure su strutture algebriche non-standard analizzando, in particolare, gli aspetti topologici...
Some problems of measure theory which are related to economic theory.
After a short discussion of the first application of measure theoretic tools to economics we show that it is consistent relative to the usual axioms of set theory that there exists no nonatomic probability space of power less than the continuum. This together with other results shows that Aumann's continuum-of-agents methodology provides a sound framework at least for the cooperative theory. There are, however, other problems in economics where, without further assumptions, the continuum may be...
Some properties od step-punctions connected with extensions of measures