Selections using orderings (non-separable case)
Semiring of Sets
Schmets [22] has developed a measure theory from a generalized notion of a semiring of sets. Goguadze [15] has introduced another generalized notion of semiring of sets and proved that all known properties that semiring have according to the old definitions are preserved. We show that this two notions are almost equivalent. We note that Patriota [20] has defined this quasi-semiring. We propose the formalization of some properties developed by the authors.
Semiring of Sets: Examples
This article proposes the formalization of some examples of semiring of sets proposed by Goguadze [8] and Schmets [13].
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 .
Sets of -porosity and sets of -porosity
Sets with no uncountable Blackwell subsets
Small non-σ-porous sets in topologically complete metric spaces
Small sets and hypercyclic vectors
We study the ``smallness'' of the set of non-hypercyclic vectors for some classical hypercyclic operators.
Small sets with respect to certain classes of topologies
Solution of a problem of Ulam on countable sequences of sets
Some additive properties of sets of real numbers
Some applications of strong Lusin sets
Some combinatorial problems on the measurability of functions with respect to invariant extensions of the Lebesgue measure
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 measure, indiscernibility and representation of cuts
Some examples of d-ideals and related Baire systems
Some operations related with translation
Some possible covers of measure zero sets
Some properties od step-punctions connected with extensions of measures