On some conditions which imply the continuity of almost all sections
Let be an open interval, a topological space and a metric space. Some local conditions implying continuity and quasicontinuity of almost all sections of a function are shown.
On some contributions to quantum structures by fuzzy sets
It is well known that the fuzzy sets theory can be successfully used in quantum models ([5, 26]). In this paper we give first a review of recent development in the probability theory on tribes and their generalizations – multivalued (MV)-algebras. Secondly we show some applications of the described method to develop probability theory on IF-events.
On some dimension problems for self-affine fractals.
On some extensions of -finite measures.
On some functional equations from additive and nonadditive measures. IV.
On some ideals and related algebras of sets in the plane
On some mappings generating vector -measures
On some numerical characterization of Boolean algebras
On some problem of A. Rosłanowski
We present a negative answer to problem 3.7(b) posed on page 193 of [2], where, in fact, A. Rosłanowski asked: Does every set of Lebesgue measure zero belong to some Mycielski ideal?
On Some Properties of Effros Borel Structure on Spaces of Closed Subsets.
On some properties of Hamel bases
On some properties of Hamel bases and their applications to Marczewski measurable functions
We introduce new properties of Hamel bases. We show that it is consistent with ZFC that such Hamel bases exist. Under the assumption that there exists a Hamel basis with one of these properties we construct a discontinuous and additive function that is Marczewski measurable. Moreover, we show that such a function can additionally have the intermediate value property (and even be an extendable function). Finally, we examine sums and limits of such functions.
On some properties of Hausdorff content related to instability.
On some properties of Hurewicz, Menger, and Rothberger
On Some Properties of Separately Increasing Functions from [0,1]ⁿ into a Banach Space
We say that a function f from [0,1] to a Banach space X is increasing with respect to E ⊂ X* if x* ∘ f is increasing for every x* ∈ E. A function is separately increasing if it is increasing in each variable separately. We show that if X is a Banach space that does not contain any isomorphic copy of c₀ or such that X* is separable, then for every separately increasing function with respect to any norming subset there exists a separately increasing function such that the sets of points of discontinuity...
On some properties of sets with positive measure
On some properties of squares of Sierpiński sets
We investigate some geometrical properties of squares of special Sierpiński sets. In particular, we prove that (under CH) there exists a Sierpiński set S and a function p: S → S such that the images of the graph of this function under π'(⟨x,y⟩) = x - y and π''(⟨x,y⟩) = x + y are both Lusin sets.
On some properties of submeasures on MV-algebras
On some properties of the Cantor set